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|---|---|---|---|
| 1 | // Copyright Contributors to the OpenVDB Project | ||
| 2 | // SPDX-License-Identifier: MPL-2.0 | ||
| 3 | |||
| 4 | /// @file math/FiniteDifference.h | ||
| 5 | |||
| 6 | #ifndef OPENVDB_MATH_FINITEDIFFERENCE_HAS_BEEN_INCLUDED | ||
| 7 | #define OPENVDB_MATH_FINITEDIFFERENCE_HAS_BEEN_INCLUDED | ||
| 8 | |||
| 9 | #include <openvdb/Types.h> | ||
| 10 | #include "Math.h" | ||
| 11 | #include "Coord.h" | ||
| 12 | #include "Vec3.h" | ||
| 13 | #include <string> | ||
| 14 | #include <boost/algorithm/string/case_conv.hpp> | ||
| 15 | #include <boost/algorithm/string/trim.hpp> | ||
| 16 | |||
| 17 | #ifdef DWA_OPENVDB | ||
| 18 | #include <simd/Simd.h> | ||
| 19 | #endif | ||
| 20 | |||
| 21 | namespace openvdb { | ||
| 22 | OPENVDB_USE_VERSION_NAMESPACE | ||
| 23 | namespace OPENVDB_VERSION_NAME { | ||
| 24 | namespace math { | ||
| 25 | |||
| 26 | |||
| 27 | //////////////////////////////////////// | ||
| 28 | |||
| 29 | |||
| 30 | /// @brief Different discrete schemes used in the first derivatives. | ||
| 31 | // Add new items to the *end* of this list, and update NUM_DS_SCHEMES. | ||
| 32 | enum DScheme { | ||
| 33 | UNKNOWN_DS = -1, | ||
| 34 | CD_2NDT = 0, // center difference, 2nd order, but the result must be divided by 2 | ||
| 35 | CD_2ND, // center difference, 2nd order | ||
| 36 | CD_4TH, // center difference, 4th order | ||
| 37 | CD_6TH, // center difference, 6th order | ||
| 38 | FD_1ST, // forward difference, 1st order | ||
| 39 | FD_2ND, // forward difference, 2nd order | ||
| 40 | FD_3RD, // forward difference, 3rd order | ||
| 41 | BD_1ST, // backward difference, 1st order | ||
| 42 | BD_2ND, // backward difference, 2nd order | ||
| 43 | BD_3RD, // backward difference, 3rd order | ||
| 44 | FD_WENO5, // forward difference, weno5 | ||
| 45 | BD_WENO5, // backward difference, weno5 | ||
| 46 | FD_HJWENO5, // forward differene, HJ-weno5 | ||
| 47 | BD_HJWENO5 // backward difference, HJ-weno5 | ||
| 48 | }; | ||
| 49 | |||
| 50 | enum { NUM_DS_SCHEMES = BD_HJWENO5 + 1 }; | ||
| 51 | |||
| 52 | |||
| 53 | inline std::string | ||
| 54 | dsSchemeToString(DScheme dss) | ||
| 55 | { | ||
| 56 | std::string ret; | ||
| 57 | switch (dss) { | ||
| 58 | case UNKNOWN_DS: ret = "unknown_ds"; break; | ||
| 59 | case CD_2NDT: ret = "cd_2ndt"; break; | ||
| 60 | case CD_2ND: ret = "cd_2nd"; break; | ||
| 61 | case CD_4TH: ret = "cd_4th"; break; | ||
| 62 | case CD_6TH: ret = "cd_6th"; break; | ||
| 63 | case FD_1ST: ret = "fd_1st"; break; | ||
| 64 | case FD_2ND: ret = "fd_2nd"; break; | ||
| 65 | case FD_3RD: ret = "fd_3rd"; break; | ||
| 66 | case BD_1ST: ret = "bd_1st"; break; | ||
| 67 | case BD_2ND: ret = "bd_2nd"; break; | ||
| 68 | case BD_3RD: ret = "bd_3rd"; break; | ||
| 69 | case FD_WENO5: ret = "fd_weno5"; break; | ||
| 70 | case BD_WENO5: ret = "bd_weno5"; break; | ||
| 71 | case FD_HJWENO5: ret = "fd_hjweno5"; break; | ||
| 72 | case BD_HJWENO5: ret = "bd_hjweno5"; break; | ||
| 73 | } | ||
| 74 | return ret; | ||
| 75 | } | ||
| 76 | |||
| 77 | inline DScheme | ||
| 78 | stringToDScheme(const std::string& s) | ||
| 79 | { | ||
| 80 | DScheme ret = UNKNOWN_DS; | ||
| 81 | |||
| 82 | std::string str = s; | ||
| 83 | boost::trim(str); | ||
| 84 | boost::to_lower(str); | ||
| 85 | |||
| 86 | if (str == dsSchemeToString(CD_2NDT)) { | ||
| 87 | ret = CD_2NDT; | ||
| 88 | } else if (str == dsSchemeToString(CD_2ND)) { | ||
| 89 | ret = CD_2ND; | ||
| 90 | } else if (str == dsSchemeToString(CD_4TH)) { | ||
| 91 | ret = CD_4TH; | ||
| 92 | } else if (str == dsSchemeToString(CD_6TH)) { | ||
| 93 | ret = CD_6TH; | ||
| 94 | } else if (str == dsSchemeToString(FD_1ST)) { | ||
| 95 | ret = FD_1ST; | ||
| 96 | } else if (str == dsSchemeToString(FD_2ND)) { | ||
| 97 | ret = FD_2ND; | ||
| 98 | } else if (str == dsSchemeToString(FD_3RD)) { | ||
| 99 | ret = FD_3RD; | ||
| 100 | } else if (str == dsSchemeToString(BD_1ST)) { | ||
| 101 | ret = BD_1ST; | ||
| 102 | } else if (str == dsSchemeToString(BD_2ND)) { | ||
| 103 | ret = BD_2ND; | ||
| 104 | } else if (str == dsSchemeToString(BD_3RD)) { | ||
| 105 | ret = BD_3RD; | ||
| 106 | } else if (str == dsSchemeToString(FD_WENO5)) { | ||
| 107 | ret = FD_WENO5; | ||
| 108 | } else if (str == dsSchemeToString(BD_WENO5)) { | ||
| 109 | ret = BD_WENO5; | ||
| 110 | } else if (str == dsSchemeToString(FD_HJWENO5)) { | ||
| 111 | ret = FD_HJWENO5; | ||
| 112 | } else if (str == dsSchemeToString(BD_HJWENO5)) { | ||
| 113 | ret = BD_HJWENO5; | ||
| 114 | } | ||
| 115 | |||
| 116 | return ret; | ||
| 117 | } | ||
| 118 | |||
| 119 | inline std::string | ||
| 120 | dsSchemeToMenuName(DScheme dss) | ||
| 121 | { | ||
| 122 | std::string ret; | ||
| 123 | switch (dss) { | ||
| 124 | case UNKNOWN_DS: ret = "Unknown DS scheme"; break; | ||
| 125 | case CD_2NDT: ret = "Twice 2nd-order center difference"; break; | ||
| 126 | case CD_2ND: ret = "2nd-order center difference"; break; | ||
| 127 | case CD_4TH: ret = "4th-order center difference"; break; | ||
| 128 | case CD_6TH: ret = "6th-order center difference"; break; | ||
| 129 | case FD_1ST: ret = "1st-order forward difference"; break; | ||
| 130 | case FD_2ND: ret = "2nd-order forward difference"; break; | ||
| 131 | case FD_3RD: ret = "3rd-order forward difference"; break; | ||
| 132 | case BD_1ST: ret = "1st-order backward difference"; break; | ||
| 133 | case BD_2ND: ret = "2nd-order backward difference"; break; | ||
| 134 | case BD_3RD: ret = "3rd-order backward difference"; break; | ||
| 135 | case FD_WENO5: ret = "5th-order WENO forward difference"; break; | ||
| 136 | case BD_WENO5: ret = "5th-order WENO backward difference"; break; | ||
| 137 | case FD_HJWENO5: ret = "5th-order HJ-WENO forward difference"; break; | ||
| 138 | case BD_HJWENO5: ret = "5th-order HJ-WENO backward difference"; break; | ||
| 139 | } | ||
| 140 | return ret; | ||
| 141 | } | ||
| 142 | |||
| 143 | |||
| 144 | |||
| 145 | //////////////////////////////////////// | ||
| 146 | |||
| 147 | |||
| 148 | /// @brief Different discrete schemes used in the second derivatives. | ||
| 149 | // Add new items to the *end* of this list, and update NUM_DD_SCHEMES. | ||
| 150 | enum DDScheme { | ||
| 151 | UNKNOWN_DD = -1, | ||
| 152 | CD_SECOND = 0, // center difference, 2nd order | ||
| 153 | CD_FOURTH, // center difference, 4th order | ||
| 154 | CD_SIXTH // center difference, 6th order | ||
| 155 | }; | ||
| 156 | |||
| 157 | enum { NUM_DD_SCHEMES = CD_SIXTH + 1 }; | ||
| 158 | |||
| 159 | |||
| 160 | //////////////////////////////////////// | ||
| 161 | |||
| 162 | |||
| 163 | /// @brief Biased Gradients are limited to non-centered differences | ||
| 164 | // Add new items to the *end* of this list, and update NUM_BIAS_SCHEMES. | ||
| 165 | enum BiasedGradientScheme { | ||
| 166 | UNKNOWN_BIAS = -1, | ||
| 167 | FIRST_BIAS = 0, // uses FD_1ST & BD_1ST | ||
| 168 | SECOND_BIAS, // uses FD_2ND & BD_2ND | ||
| 169 | THIRD_BIAS, // uses FD_3RD & BD_3RD | ||
| 170 | WENO5_BIAS, // uses WENO5 | ||
| 171 | HJWENO5_BIAS // uses HJWENO5 | ||
| 172 | }; | ||
| 173 | |||
| 174 | enum { NUM_BIAS_SCHEMES = HJWENO5_BIAS + 1 }; | ||
| 175 | |||
| 176 | inline std::string | ||
| 177 | biasedGradientSchemeToString(BiasedGradientScheme bgs) | ||
| 178 | { | ||
| 179 | std::string ret; | ||
| 180 | switch (bgs) { | ||
| 181 | case UNKNOWN_BIAS: ret = "unknown_bias"; break; | ||
| 182 | case FIRST_BIAS: ret = "first_bias"; break; | ||
| 183 | case SECOND_BIAS: ret = "second_bias"; break; | ||
| 184 | case THIRD_BIAS: ret = "third_bias"; break; | ||
| 185 | case WENO5_BIAS: ret = "weno5_bias"; break; | ||
| 186 | case HJWENO5_BIAS: ret = "hjweno5_bias"; break; | ||
| 187 | } | ||
| 188 | return ret; | ||
| 189 | } | ||
| 190 | |||
| 191 | inline BiasedGradientScheme | ||
| 192 | stringToBiasedGradientScheme(const std::string& s) | ||
| 193 | { | ||
| 194 | BiasedGradientScheme ret = UNKNOWN_BIAS; | ||
| 195 | |||
| 196 | std::string str = s; | ||
| 197 | boost::trim(str); | ||
| 198 | boost::to_lower(str); | ||
| 199 | |||
| 200 | if (str == biasedGradientSchemeToString(FIRST_BIAS)) { | ||
| 201 | ret = FIRST_BIAS; | ||
| 202 | } else if (str == biasedGradientSchemeToString(SECOND_BIAS)) { | ||
| 203 | ret = SECOND_BIAS; | ||
| 204 | } else if (str == biasedGradientSchemeToString(THIRD_BIAS)) { | ||
| 205 | ret = THIRD_BIAS; | ||
| 206 | } else if (str == biasedGradientSchemeToString(WENO5_BIAS)) { | ||
| 207 | ret = WENO5_BIAS; | ||
| 208 | } else if (str == biasedGradientSchemeToString(HJWENO5_BIAS)) { | ||
| 209 | ret = HJWENO5_BIAS; | ||
| 210 | } | ||
| 211 | return ret; | ||
| 212 | } | ||
| 213 | |||
| 214 | inline std::string | ||
| 215 | biasedGradientSchemeToMenuName(BiasedGradientScheme bgs) | ||
| 216 | { | ||
| 217 | std::string ret; | ||
| 218 | switch (bgs) { | ||
| 219 | case UNKNOWN_BIAS: ret = "Unknown biased gradient"; break; | ||
| 220 | case FIRST_BIAS: ret = "1st-order biased gradient"; break; | ||
| 221 | case SECOND_BIAS: ret = "2nd-order biased gradient"; break; | ||
| 222 | case THIRD_BIAS: ret = "3rd-order biased gradient"; break; | ||
| 223 | case WENO5_BIAS: ret = "5th-order WENO biased gradient"; break; | ||
| 224 | case HJWENO5_BIAS: ret = "5th-order HJ-WENO biased gradient"; break; | ||
| 225 | } | ||
| 226 | return ret; | ||
| 227 | } | ||
| 228 | |||
| 229 | //////////////////////////////////////// | ||
| 230 | |||
| 231 | |||
| 232 | /// @brief Temporal integration schemes | ||
| 233 | // Add new items to the *end* of this list, and update NUM_TEMPORAL_SCHEMES. | ||
| 234 | enum TemporalIntegrationScheme { | ||
| 235 | UNKNOWN_TIS = -1, | ||
| 236 | TVD_RK1,//same as explicit Euler integration | ||
| 237 | TVD_RK2, | ||
| 238 | TVD_RK3 | ||
| 239 | }; | ||
| 240 | |||
| 241 | enum { NUM_TEMPORAL_SCHEMES = TVD_RK3 + 1 }; | ||
| 242 | |||
| 243 | inline std::string | ||
| 244 | temporalIntegrationSchemeToString(TemporalIntegrationScheme tis) | ||
| 245 | { | ||
| 246 | std::string ret; | ||
| 247 | switch (tis) { | ||
| 248 | case UNKNOWN_TIS: ret = "unknown_tis"; break; | ||
| 249 | case TVD_RK1: ret = "tvd_rk1"; break; | ||
| 250 | case TVD_RK2: ret = "tvd_rk2"; break; | ||
| 251 | case TVD_RK3: ret = "tvd_rk3"; break; | ||
| 252 | } | ||
| 253 | return ret; | ||
| 254 | } | ||
| 255 | |||
| 256 | inline TemporalIntegrationScheme | ||
| 257 | stringToTemporalIntegrationScheme(const std::string& s) | ||
| 258 | { | ||
| 259 | TemporalIntegrationScheme ret = UNKNOWN_TIS; | ||
| 260 | |||
| 261 | std::string str = s; | ||
| 262 | boost::trim(str); | ||
| 263 | boost::to_lower(str); | ||
| 264 | |||
| 265 | if (str == temporalIntegrationSchemeToString(TVD_RK1)) { | ||
| 266 | ret = TVD_RK1; | ||
| 267 | } else if (str == temporalIntegrationSchemeToString(TVD_RK2)) { | ||
| 268 | ret = TVD_RK2; | ||
| 269 | } else if (str == temporalIntegrationSchemeToString(TVD_RK3)) { | ||
| 270 | ret = TVD_RK3; | ||
| 271 | } | ||
| 272 | |||
| 273 | return ret; | ||
| 274 | } | ||
| 275 | |||
| 276 | inline std::string | ||
| 277 | temporalIntegrationSchemeToMenuName(TemporalIntegrationScheme tis) | ||
| 278 | { | ||
| 279 | std::string ret; | ||
| 280 | switch (tis) { | ||
| 281 | case UNKNOWN_TIS: ret = "Unknown temporal integration"; break; | ||
| 282 | case TVD_RK1: ret = "Forward Euler"; break; | ||
| 283 | case TVD_RK2: ret = "2nd-order Runge-Kutta"; break; | ||
| 284 | case TVD_RK3: ret = "3rd-order Runge-Kutta"; break; | ||
| 285 | } | ||
| 286 | return ret; | ||
| 287 | } | ||
| 288 | |||
| 289 | |||
| 290 | //@} | ||
| 291 | |||
| 292 | |||
| 293 | /// @brief Implementation of nominally fifth-order finite-difference WENO | ||
| 294 | /// @details This function returns the numerical flux. See "High Order Finite Difference and | ||
| 295 | /// Finite Volume WENO Schemes and Discontinuous Galerkin Methods for CFD" - Chi-Wang Shu | ||
| 296 | /// ICASE Report No 2001-11 (page 6). Also see ICASE No 97-65 for a more complete reference | ||
| 297 | /// (Shu, 1997). | ||
| 298 | /// Given v1 = f(x-2dx), v2 = f(x-dx), v3 = f(x), v4 = f(x+dx) and v5 = f(x+2dx), | ||
| 299 | /// return an interpolated value f(x+dx/2) with the special property that | ||
| 300 | /// ( f(x+dx/2) - f(x-dx/2) ) / dx = df/dx (x) + error, | ||
| 301 | /// where the error is fifth-order in smooth regions: O(dx) <= error <=O(dx^5) | ||
| 302 | template<typename ValueType> | ||
| 303 | inline ValueType | ||
| 304 | 14847354 | WENO5(const ValueType& v1, const ValueType& v2, const ValueType& v3, | |
| 305 | const ValueType& v4, const ValueType& v5, float scale2 = 0.01f) | ||
| 306 | { | ||
| 307 | const double C = 13.0 / 12.0; | ||
| 308 | // WENO is formulated for non-dimensional equations, here the optional scale2 | ||
| 309 | // is a reference value (squared) for the function being interpolated. For | ||
| 310 | // example if 'v' is of order 1000, then scale2 = 10^6 is ok. But in practice | ||
| 311 | // leave scale2 = 1. | ||
| 312 | 14847354 | const double eps = 1.0e-6 * static_cast<double>(scale2); | |
| 313 | // {\tilde \omega_k} = \gamma_k / ( \beta_k + \epsilon)^2 in Shu's ICASE report) | ||
| 314 | 14847354 | const double A1=0.1/math::Pow2(C*math::Pow2(v1-2*v2+v3)+0.25*math::Pow2(v1-4*v2+3.0*v3)+eps), | |
| 315 | 14847354 | A2=0.6/math::Pow2(C*math::Pow2(v2-2*v3+v4)+0.25*math::Pow2(v2-v4)+eps), | |
| 316 | 14847354 | A3=0.3/math::Pow2(C*math::Pow2(v3-2*v4+v5)+0.25*math::Pow2(3.0*v3-4*v4+v5)+eps); | |
| 317 | |||
| 318 | return static_cast<ValueType>(static_cast<ValueType>( | ||
| 319 | 14847354 | A1*(2.0*v1 - 7.0*v2 + 11.0*v3) + | |
| 320 | 14847354 | A2*(5.0*v3 - v2 + 2.0*v4) + | |
| 321 | 14847354 | A3*(2.0*v3 + 5.0*v4 - v5))/(6.0*(A1+A2+A3))); | |
| 322 | } | ||
| 323 | |||
| 324 | |||
| 325 | template <typename Real> | ||
| 326 | 22448213 | inline Real GodunovsNormSqrd(bool isOutside, | |
| 327 | Real dP_xm, Real dP_xp, | ||
| 328 | Real dP_ym, Real dP_yp, | ||
| 329 | Real dP_zm, Real dP_zp) | ||
| 330 | { | ||
| 331 | using math::Max; | ||
| 332 | using math::Min; | ||
| 333 | using math::Pow2; | ||
| 334 | |||
| 335 | 22448213 | const Real zero(0); | |
| 336 | Real dPLen2; | ||
| 337 |
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22448213 | if (isOutside) { // outside |
| 338 |
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19790812 | dPLen2 = Max(Pow2(Max(dP_xm, zero)), Pow2(Min(dP_xp,zero))); // (dP/dx)2 |
| 339 |
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20420812 | dPLen2 += Max(Pow2(Max(dP_ym, zero)), Pow2(Min(dP_yp,zero))); // (dP/dy)2 |
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20465735 | dPLen2 += Max(Pow2(Max(dP_zm, zero)), Pow2(Min(dP_zp,zero))); // (dP/dz)2 |
| 341 | } else { // inside | ||
| 342 |
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20427612 | dPLen2 = Max(Pow2(Min(dP_xm, zero)), Pow2(Max(dP_xp,zero))); // (dP/dx)2 |
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20198526 | dPLen2 += Max(Pow2(Min(dP_ym, zero)), Pow2(Max(dP_yp,zero))); // (dP/dy)2 |
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20212750 | dPLen2 += Max(Pow2(Min(dP_zm, zero)), Pow2(Max(dP_zp,zero))); // (dP/dz)2 |
| 345 | } | ||
| 346 | 22448213 | return dPLen2; // |\nabla\phi|^2 | |
| 347 | } | ||
| 348 | |||
| 349 | |||
| 350 | template<typename Real> | ||
| 351 | inline Real | ||
| 352 | GodunovsNormSqrd(bool isOutside, const Vec3<Real>& gradient_m, const Vec3<Real>& gradient_p) | ||
| 353 | { | ||
| 354 | 11490754 | return GodunovsNormSqrd<Real>(isOutside, | |
| 355 | gradient_m[0], gradient_p[0], | ||
| 356 | gradient_m[1], gradient_p[1], | ||
| 357 | gradient_m[2], gradient_p[2]); | ||
| 358 | } | ||
| 359 | |||
| 360 | |||
| 361 | #ifdef DWA_OPENVDB | ||
| 362 | inline simd::Float4 simdMin(const simd::Float4& a, const simd::Float4& b) { | ||
| 363 | return simd::Float4(_mm_min_ps(a.base(), b.base())); | ||
| 364 | } | ||
| 365 | inline simd::Float4 simdMax(const simd::Float4& a, const simd::Float4& b) { | ||
| 366 | return simd::Float4(_mm_max_ps(a.base(), b.base())); | ||
| 367 | } | ||
| 368 | |||
| 369 | inline float simdSum(const simd::Float4& v); | ||
| 370 | |||
| 371 | inline simd::Float4 Pow2(const simd::Float4& v) { return v * v; } | ||
| 372 | |||
| 373 | template<> | ||
| 374 | inline simd::Float4 | ||
| 375 | WENO5<simd::Float4>(const simd::Float4& v1, const simd::Float4& v2, const simd::Float4& v3, | ||
| 376 | const simd::Float4& v4, const simd::Float4& v5, float scale2) | ||
| 377 | { | ||
| 378 | using math::Pow2; | ||
| 379 | using F4 = simd::Float4; | ||
| 380 | const F4 | ||
| 381 | C(13.f / 12.f), | ||
| 382 | eps(1.0e-6f * scale2), | ||
| 383 | two(2.0), three(3.0), four(4.0), five(5.0), fourth(0.25), | ||
| 384 | A1 = F4(0.1f) / Pow2(C*Pow2(v1-two*v2+v3) + fourth*Pow2(v1-four*v2+three*v3) + eps), | ||
| 385 | A2 = F4(0.6f) / Pow2(C*Pow2(v2-two*v3+v4) + fourth*Pow2(v2-v4) + eps), | ||
| 386 | A3 = F4(0.3f) / Pow2(C*Pow2(v3-two*v4+v5) + fourth*Pow2(three*v3-four*v4+v5) + eps); | ||
| 387 | return (A1 * (two * v1 - F4(7.0) * v2 + F4(11.0) * v3) + | ||
| 388 | A2 * (five * v3 - v2 + two * v4) + | ||
| 389 | A3 * (two * v3 + five * v4 - v5)) / (F4(6.0) * (A1 + A2 + A3)); | ||
| 390 | } | ||
| 391 | |||
| 392 | |||
| 393 | inline float | ||
| 394 | simdSum(const simd::Float4& v) | ||
| 395 | { | ||
| 396 | // temp = { v3+v3, v2+v2, v1+v3, v0+v2 } | ||
| 397 | __m128 temp = _mm_add_ps(v.base(), _mm_movehl_ps(v.base(), v.base())); | ||
| 398 | // temp = { v3+v3, v2+v2, v1+v3, (v0+v2)+(v1+v3) } | ||
| 399 | temp = _mm_add_ss(temp, _mm_shuffle_ps(temp, temp, 1)); | ||
| 400 | return _mm_cvtss_f32(temp); | ||
| 401 | } | ||
| 402 | |||
| 403 | inline float | ||
| 404 | GodunovsNormSqrd(bool isOutside, const simd::Float4& dP_m, const simd::Float4& dP_p) | ||
| 405 | { | ||
| 406 | const simd::Float4 zero(0.0); | ||
| 407 | simd::Float4 v = isOutside | ||
| 408 | ? simdMax(math::Pow2(simdMax(dP_m, zero)), math::Pow2(simdMin(dP_p, zero))) | ||
| 409 | : simdMax(math::Pow2(simdMin(dP_m, zero)), math::Pow2(simdMax(dP_p, zero))); | ||
| 410 | return simdSum(v);//should be v[0]+v[1]+v[2] | ||
| 411 | } | ||
| 412 | #endif | ||
| 413 | |||
| 414 | |||
| 415 | template<DScheme DiffScheme> | ||
| 416 | struct D1 | ||
| 417 | { | ||
| 418 | // random access version | ||
| 419 | template<typename Accessor> | ||
| 420 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk); | ||
| 421 | |||
| 422 | template<typename Accessor> | ||
| 423 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk); | ||
| 424 | |||
| 425 | template<typename Accessor> | ||
| 426 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk); | ||
| 427 | |||
| 428 | // stencil access version | ||
| 429 | template<typename Stencil> | ||
| 430 | static typename Stencil::ValueType inX(const Stencil& S); | ||
| 431 | |||
| 432 | template<typename Stencil> | ||
| 433 | static typename Stencil::ValueType inY(const Stencil& S); | ||
| 434 | |||
| 435 | template<typename Stencil> | ||
| 436 | static typename Stencil::ValueType inZ(const Stencil& S); | ||
| 437 | }; | ||
| 438 | |||
| 439 | template<> | ||
| 440 | struct D1<CD_2NDT> | ||
| 441 | { | ||
| 442 | // the difference opperator | ||
| 443 | template <typename ValueType> | ||
| 444 | static ValueType difference(const ValueType& xp1, const ValueType& xm1) { | ||
| 445 |
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21393698 | return xp1 - xm1; |
| 446 | } | ||
| 447 | |||
| 448 | // random access version | ||
| 449 | template<typename Accessor> | ||
| 450 | 11977458 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 451 | { | ||
| 452 | 11977420 | return difference( | |
| 453 | 11977458 | grid.getValue(ijk.offsetBy(1, 0, 0)), | |
| 454 | 11977458 | grid.getValue(ijk.offsetBy(-1, 0, 0))); | |
| 455 | } | ||
| 456 | |||
| 457 | template<typename Accessor> | ||
| 458 | 11977458 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 459 | { | ||
| 460 | 11977420 | return difference( | |
| 461 | 11977458 | grid.getValue(ijk.offsetBy(0, 1, 0)), | |
| 462 | 11977458 | grid.getValue(ijk.offsetBy( 0, -1, 0))); | |
| 463 | } | ||
| 464 | |||
| 465 | template<typename Accessor> | ||
| 466 | 11977458 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 467 | { | ||
| 468 | 11977420 | return difference( | |
| 469 | 11977458 | grid.getValue(ijk.offsetBy(0, 0, 1)), | |
| 470 | 11977458 | grid.getValue(ijk.offsetBy( 0, 0, -1))); | |
| 471 | } | ||
| 472 | |||
| 473 | // stencil access version | ||
| 474 | template<typename Stencil> | ||
| 475 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 476 | { | ||
| 477 | return difference( S.template getValue< 1, 0, 0>(), S.template getValue<-1, 0, 0>()); | ||
| 478 | } | ||
| 479 | |||
| 480 | template<typename Stencil> | ||
| 481 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 482 | { | ||
| 483 | return difference( S.template getValue< 0, 1, 0>(), S.template getValue< 0,-1, 0>()); | ||
| 484 | } | ||
| 485 | |||
| 486 | template<typename Stencil> | ||
| 487 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 488 | { | ||
| 489 | return difference( S.template getValue< 0, 0, 1>(), S.template getValue< 0, 0,-1>()); | ||
| 490 | } | ||
| 491 | }; | ||
| 492 | |||
| 493 | template<> | ||
| 494 | struct D1<CD_2ND> | ||
| 495 | { | ||
| 496 | |||
| 497 | // the difference opperator | ||
| 498 | template <typename ValueType> | ||
| 499 | static ValueType difference(const ValueType& xp1, const ValueType& xm1) { | ||
| 500 |
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941179 | return (xp1 - xm1)*ValueType(0.5); |
| 501 | } | ||
| 502 | static bool difference(const bool& xp1, const bool& /*xm1*/) { | ||
| 503 | ✗ | return xp1; | |
| 504 | } | ||
| 505 | |||
| 506 | |||
| 507 | // random access | ||
| 508 | template<typename Accessor> | ||
| 509 | 526363 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 510 | { | ||
| 511 | 526357 | return difference( | |
| 512 | 526363 | grid.getValue(ijk.offsetBy(1, 0, 0)), | |
| 513 | 526363 | grid.getValue(ijk.offsetBy(-1, 0, 0))); | |
| 514 | } | ||
| 515 | |||
| 516 | template<typename Accessor> | ||
| 517 | 526363 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 518 | { | ||
| 519 | 526357 | return difference( | |
| 520 | 526363 | grid.getValue(ijk.offsetBy(0, 1, 0)), | |
| 521 | 526363 | grid.getValue(ijk.offsetBy( 0, -1, 0))); | |
| 522 | } | ||
| 523 | |||
| 524 | template<typename Accessor> | ||
| 525 | 526348 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 526 | { | ||
| 527 | 526342 | return difference( | |
| 528 | 526348 | grid.getValue(ijk.offsetBy(0, 0, 1)), | |
| 529 | 526348 | grid.getValue(ijk.offsetBy( 0, 0, -1))); | |
| 530 | } | ||
| 531 | |||
| 532 | |||
| 533 | // stencil access version | ||
| 534 | template<typename Stencil> | ||
| 535 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 536 | { | ||
| 537 | return difference(S.template getValue< 1, 0, 0>(), S.template getValue<-1, 0, 0>()); | ||
| 538 | } | ||
| 539 | template<typename Stencil> | ||
| 540 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 541 | { | ||
| 542 | return difference(S.template getValue< 0, 1, 0>(), S.template getValue< 0,-1, 0>()); | ||
| 543 | } | ||
| 544 | |||
| 545 | template<typename Stencil> | ||
| 546 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 547 | { | ||
| 548 | return difference(S.template getValue< 0, 0, 1>(), S.template getValue< 0, 0,-1>()); | ||
| 549 | } | ||
| 550 | |||
| 551 | }; | ||
| 552 | |||
| 553 | template<> | ||
| 554 | struct D1<CD_4TH> | ||
| 555 | { | ||
| 556 | |||
| 557 | // the difference opperator | ||
| 558 | template <typename ValueType> | ||
| 559 | static ValueType difference( const ValueType& xp2, const ValueType& xp1, | ||
| 560 | const ValueType& xm1, const ValueType& xm2 ) { | ||
| 561 |
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73874 | return ValueType(2./3.)*(xp1 - xm1) + ValueType(1./12.)*(xm2 - xp2) ; |
| 562 | } | ||
| 563 | |||
| 564 | |||
| 565 | // random access version | ||
| 566 | template<typename Accessor> | ||
| 567 | 84 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 568 | { | ||
| 569 | 84 | return difference( | |
| 570 | 84 | grid.getValue(ijk.offsetBy( 2,0,0)), grid.getValue(ijk.offsetBy( 1,0,0)), | |
| 571 | 84 | grid.getValue(ijk.offsetBy(-1,0,0)), grid.getValue(ijk.offsetBy(-2,0,0)) ); | |
| 572 | } | ||
| 573 | |||
| 574 | template<typename Accessor> | ||
| 575 | 48 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 576 | { | ||
| 577 | |||
| 578 | 48 | return difference( | |
| 579 | 48 | grid.getValue(ijk.offsetBy( 0, 2, 0)), grid.getValue(ijk.offsetBy( 0, 1, 0)), | |
| 580 | 48 | grid.getValue(ijk.offsetBy( 0,-1, 0)), grid.getValue(ijk.offsetBy( 0,-2, 0)) ); | |
| 581 | } | ||
| 582 | |||
| 583 | template<typename Accessor> | ||
| 584 | 12 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 585 | { | ||
| 586 | |||
| 587 | 12 | return difference( | |
| 588 | 12 | grid.getValue(ijk.offsetBy( 0, 0, 2)), grid.getValue(ijk.offsetBy( 0, 0, 1)), | |
| 589 | 12 | grid.getValue(ijk.offsetBy( 0, 0,-1)), grid.getValue(ijk.offsetBy( 0, 0,-2)) ); | |
| 590 | } | ||
| 591 | |||
| 592 | |||
| 593 | // stencil access version | ||
| 594 | template<typename Stencil> | ||
| 595 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 596 | { | ||
| 597 | return difference( S.template getValue< 2, 0, 0>(), | ||
| 598 | S.template getValue< 1, 0, 0>(), | ||
| 599 | S.template getValue<-1, 0, 0>(), | ||
| 600 | S.template getValue<-2, 0, 0>() ); | ||
| 601 | } | ||
| 602 | |||
| 603 | template<typename Stencil> | ||
| 604 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 605 | { | ||
| 606 | return difference( S.template getValue< 0, 2, 0>(), | ||
| 607 | S.template getValue< 0, 1, 0>(), | ||
| 608 | S.template getValue< 0,-1, 0>(), | ||
| 609 | S.template getValue< 0,-2, 0>() ); | ||
| 610 | } | ||
| 611 | |||
| 612 | template<typename Stencil> | ||
| 613 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 614 | { | ||
| 615 | return difference( S.template getValue< 0, 0, 2>(), | ||
| 616 | S.template getValue< 0, 0, 1>(), | ||
| 617 | S.template getValue< 0, 0,-1>(), | ||
| 618 | S.template getValue< 0, 0,-2>() ); | ||
| 619 | } | ||
| 620 | }; | ||
| 621 | |||
| 622 | template<> | ||
| 623 | struct D1<CD_6TH> | ||
| 624 | { | ||
| 625 | |||
| 626 | // the difference opperator | ||
| 627 | template <typename ValueType> | ||
| 628 | static ValueType difference( const ValueType& xp3, const ValueType& xp2, const ValueType& xp1, | ||
| 629 | const ValueType& xm1, const ValueType& xm2, const ValueType& xm3 ) | ||
| 630 | { | ||
| 631 | 49588 | return ValueType(3./4.)*(xp1 - xm1) - ValueType(0.15)*(xp2 - xm2) | |
| 632 |
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49576 | + ValueType(1./60.)*(xp3-xm3); |
| 633 | } | ||
| 634 | |||
| 635 | |||
| 636 | // random access version | ||
| 637 | template<typename Accessor> | ||
| 638 | 109 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 639 | { | ||
| 640 | 109 | return difference( | |
| 641 | 109 | grid.getValue(ijk.offsetBy( 3,0,0)), grid.getValue(ijk.offsetBy( 2,0,0)), | |
| 642 | 109 | grid.getValue(ijk.offsetBy( 1,0,0)), grid.getValue(ijk.offsetBy(-1,0,0)), | |
| 643 | 109 | grid.getValue(ijk.offsetBy(-2,0,0)), grid.getValue(ijk.offsetBy(-3,0,0))); | |
| 644 | } | ||
| 645 | |||
| 646 | template<typename Accessor> | ||
| 647 | 61 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 648 | { | ||
| 649 | 61 | return difference( | |
| 650 | 61 | grid.getValue(ijk.offsetBy( 0, 3, 0)), grid.getValue(ijk.offsetBy( 0, 2, 0)), | |
| 651 | 61 | grid.getValue(ijk.offsetBy( 0, 1, 0)), grid.getValue(ijk.offsetBy( 0,-1, 0)), | |
| 652 | 61 | grid.getValue(ijk.offsetBy( 0,-2, 0)), grid.getValue(ijk.offsetBy( 0,-3, 0))); | |
| 653 | } | ||
| 654 | |||
| 655 | template<typename Accessor> | ||
| 656 | 13 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 657 | { | ||
| 658 | 13 | return difference( | |
| 659 | 13 | grid.getValue(ijk.offsetBy( 0, 0, 3)), grid.getValue(ijk.offsetBy( 0, 0, 2)), | |
| 660 | 13 | grid.getValue(ijk.offsetBy( 0, 0, 1)), grid.getValue(ijk.offsetBy( 0, 0,-1)), | |
| 661 | 13 | grid.getValue(ijk.offsetBy( 0, 0,-2)), grid.getValue(ijk.offsetBy( 0, 0,-3))); | |
| 662 | } | ||
| 663 | |||
| 664 | // stencil access version | ||
| 665 | template<typename Stencil> | ||
| 666 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 667 | { | ||
| 668 | return difference(S.template getValue< 3, 0, 0>(), | ||
| 669 | S.template getValue< 2, 0, 0>(), | ||
| 670 | S.template getValue< 1, 0, 0>(), | ||
| 671 | S.template getValue<-1, 0, 0>(), | ||
| 672 | S.template getValue<-2, 0, 0>(), | ||
| 673 | S.template getValue<-3, 0, 0>()); | ||
| 674 | } | ||
| 675 | |||
| 676 | template<typename Stencil> | ||
| 677 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 678 | { | ||
| 679 | |||
| 680 | return difference( S.template getValue< 0, 3, 0>(), | ||
| 681 | S.template getValue< 0, 2, 0>(), | ||
| 682 | S.template getValue< 0, 1, 0>(), | ||
| 683 | S.template getValue< 0,-1, 0>(), | ||
| 684 | S.template getValue< 0,-2, 0>(), | ||
| 685 | S.template getValue< 0,-3, 0>()); | ||
| 686 | } | ||
| 687 | |||
| 688 | template<typename Stencil> | ||
| 689 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 690 | { | ||
| 691 | |||
| 692 | return difference( S.template getValue< 0, 0, 3>(), | ||
| 693 | S.template getValue< 0, 0, 2>(), | ||
| 694 | S.template getValue< 0, 0, 1>(), | ||
| 695 | S.template getValue< 0, 0,-1>(), | ||
| 696 | S.template getValue< 0, 0,-2>(), | ||
| 697 | S.template getValue< 0, 0,-3>()); | ||
| 698 | } | ||
| 699 | }; | ||
| 700 | |||
| 701 | |||
| 702 | template<> | ||
| 703 | struct D1<FD_1ST> | ||
| 704 | { | ||
| 705 | |||
| 706 | // the difference opperator | ||
| 707 | template <typename ValueType> | ||
| 708 | static ValueType difference(const ValueType& xp1, const ValueType& xp0) { | ||
| 709 |
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114270335 | return xp1 - xp0; |
| 710 | } | ||
| 711 | |||
| 712 | |||
| 713 | // random access version | ||
| 714 | template<typename Accessor> | ||
| 715 | 115565654 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 716 | { | ||
| 717 | 115565654 | return difference(grid.getValue(ijk.offsetBy(1, 0, 0)), grid.getValue(ijk)); | |
| 718 | } | ||
| 719 | |||
| 720 | template<typename Accessor> | ||
| 721 | 115565654 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 722 | { | ||
| 723 | 115565654 | return difference(grid.getValue(ijk.offsetBy(0, 1, 0)), grid.getValue(ijk)); | |
| 724 | } | ||
| 725 | |||
| 726 | template<typename Accessor> | ||
| 727 | 115565654 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 728 | { | ||
| 729 | 115565654 | return difference(grid.getValue(ijk.offsetBy(0, 0, 1)), grid.getValue(ijk)); | |
| 730 | } | ||
| 731 | |||
| 732 | // stencil access version | ||
| 733 | template<typename Stencil> | ||
| 734 | 186624 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 735 | { | ||
| 736 | 186624 | return difference(S.template getValue< 1, 0, 0>(), S.template getValue< 0, 0, 0>()); | |
| 737 | } | ||
| 738 | |||
| 739 | template<typename Stencil> | ||
| 740 | 186624 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 741 | { | ||
| 742 | 186624 | return difference(S.template getValue< 0, 1, 0>(), S.template getValue< 0, 0, 0>()); | |
| 743 | } | ||
| 744 | |||
| 745 | template<typename Stencil> | ||
| 746 | 186624 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 747 | { | ||
| 748 | 186624 | return difference(S.template getValue< 0, 0, 1>(), S.template getValue< 0, 0, 0>()); | |
| 749 | } | ||
| 750 | }; | ||
| 751 | |||
| 752 | |||
| 753 | template<> | ||
| 754 | struct D1<FD_2ND> | ||
| 755 | { | ||
| 756 | // the difference opperator | ||
| 757 | template <typename ValueType> | ||
| 758 | 147456 | static ValueType difference(const ValueType& xp2, const ValueType& xp1, const ValueType& xp0) | |
| 759 | { | ||
| 760 | 147472 | return ValueType(2)*xp1 -(ValueType(0.5)*xp2 + ValueType(3./2.)*xp0); | |
| 761 | } | ||
| 762 | |||
| 763 | |||
| 764 | // random access version | ||
| 765 | template<typename Accessor> | ||
| 766 | 12290 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 767 | { | ||
| 768 | 12290 | return difference( | |
| 769 | 12290 | grid.getValue(ijk.offsetBy(2,0,0)), | |
| 770 | 12290 | grid.getValue(ijk.offsetBy(1,0,0)), | |
| 771 | 12290 | grid.getValue(ijk)); | |
| 772 | } | ||
| 773 | |||
| 774 | template<typename Accessor> | ||
| 775 | 12290 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 776 | { | ||
| 777 | 12290 | return difference( | |
| 778 | 12290 | grid.getValue(ijk.offsetBy(0,2,0)), | |
| 779 | 12290 | grid.getValue(ijk.offsetBy(0,1,0)), | |
| 780 | 12290 | grid.getValue(ijk)); | |
| 781 | } | ||
| 782 | |||
| 783 | template<typename Accessor> | ||
| 784 | 12290 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 785 | { | ||
| 786 | 12290 | return difference( | |
| 787 | 12290 | grid.getValue(ijk.offsetBy(0,0,2)), | |
| 788 | 12290 | grid.getValue(ijk.offsetBy(0,0,1)), | |
| 789 | 12290 | grid.getValue(ijk)); | |
| 790 | } | ||
| 791 | |||
| 792 | |||
| 793 | // stencil access version | ||
| 794 | template<typename Stencil> | ||
| 795 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 796 | { | ||
| 797 | 12288 | return difference( S.template getValue< 2, 0, 0>(), | |
| 798 | S.template getValue< 1, 0, 0>(), | ||
| 799 | S.template getValue< 0, 0, 0>() ); | ||
| 800 | } | ||
| 801 | |||
| 802 | template<typename Stencil> | ||
| 803 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 804 | { | ||
| 805 | 12288 | return difference( S.template getValue< 0, 2, 0>(), | |
| 806 | S.template getValue< 0, 1, 0>(), | ||
| 807 | S.template getValue< 0, 0, 0>() ); | ||
| 808 | } | ||
| 809 | |||
| 810 | template<typename Stencil> | ||
| 811 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 812 | { | ||
| 813 | 12288 | return difference( S.template getValue< 0, 0, 2>(), | |
| 814 | S.template getValue< 0, 0, 1>(), | ||
| 815 | S.template getValue< 0, 0, 0>() ); | ||
| 816 | } | ||
| 817 | |||
| 818 | }; | ||
| 819 | |||
| 820 | |||
| 821 | template<> | ||
| 822 | struct D1<FD_3RD> | ||
| 823 | { | ||
| 824 | |||
| 825 | // the difference opperator | ||
| 826 | template<typename ValueType> | ||
| 827 | 98784 | static ValueType difference(const ValueType& xp3, const ValueType& xp2, | |
| 828 | const ValueType& xp1, const ValueType& xp0) | ||
| 829 | { | ||
| 830 | 98800 | return static_cast<ValueType>(xp3/3.0 - 1.5*xp2 + 3.0*xp1 - 11.0*xp0/6.0); | |
| 831 | } | ||
| 832 | |||
| 833 | |||
| 834 | // random access version | ||
| 835 | template<typename Accessor> | ||
| 836 | 8234 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 837 | { | ||
| 838 | 16468 | return difference( grid.getValue(ijk.offsetBy(3,0,0)), | |
| 839 | 8234 | grid.getValue(ijk.offsetBy(2,0,0)), | |
| 840 | 8234 | grid.getValue(ijk.offsetBy(1,0,0)), | |
| 841 | 8234 | grid.getValue(ijk) ); | |
| 842 | } | ||
| 843 | |||
| 844 | template<typename Accessor> | ||
| 845 | 8234 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 846 | { | ||
| 847 | 16468 | return difference( grid.getValue(ijk.offsetBy(0,3,0)), | |
| 848 | 8234 | grid.getValue(ijk.offsetBy(0,2,0)), | |
| 849 | 8234 | grid.getValue(ijk.offsetBy(0,1,0)), | |
| 850 | 8234 | grid.getValue(ijk) ); | |
| 851 | } | ||
| 852 | |||
| 853 | template<typename Accessor> | ||
| 854 | 8234 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 855 | { | ||
| 856 | 16468 | return difference( grid.getValue(ijk.offsetBy(0,0,3)), | |
| 857 | 8234 | grid.getValue(ijk.offsetBy(0,0,2)), | |
| 858 | 8234 | grid.getValue(ijk.offsetBy(0,0,1)), | |
| 859 | 8234 | grid.getValue(ijk) ); | |
| 860 | } | ||
| 861 | |||
| 862 | |||
| 863 | // stencil access version | ||
| 864 | template<typename Stencil> | ||
| 865 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 866 | { | ||
| 867 | 8232 | return difference(S.template getValue< 3, 0, 0>(), | |
| 868 | S.template getValue< 2, 0, 0>(), | ||
| 869 | S.template getValue< 1, 0, 0>(), | ||
| 870 | S.template getValue< 0, 0, 0>() ); | ||
| 871 | } | ||
| 872 | |||
| 873 | template<typename Stencil> | ||
| 874 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 875 | { | ||
| 876 | 8232 | return difference(S.template getValue< 0, 3, 0>(), | |
| 877 | S.template getValue< 0, 2, 0>(), | ||
| 878 | S.template getValue< 0, 1, 0>(), | ||
| 879 | S.template getValue< 0, 0, 0>() ); | ||
| 880 | } | ||
| 881 | |||
| 882 | template<typename Stencil> | ||
| 883 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 884 | { | ||
| 885 | 8232 | return difference( S.template getValue< 0, 0, 3>(), | |
| 886 | S.template getValue< 0, 0, 2>(), | ||
| 887 | S.template getValue< 0, 0, 1>(), | ||
| 888 | S.template getValue< 0, 0, 0>() ); | ||
| 889 | } | ||
| 890 | }; | ||
| 891 | |||
| 892 | |||
| 893 | template<> | ||
| 894 | struct D1<BD_1ST> | ||
| 895 | { | ||
| 896 | |||
| 897 | // the difference opperator | ||
| 898 | template <typename ValueType> | ||
| 899 | 559872 | static ValueType difference(const ValueType& xm1, const ValueType& xm0) { | |
| 900 |
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17229236 | return -D1<FD_1ST>::difference(xm1, xm0); |
| 901 | } | ||
| 902 | |||
| 903 | |||
| 904 | // random access version | ||
| 905 | template<typename Accessor> | ||
| 906 | 5671060 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 907 | { | ||
| 908 | 5671060 | return difference(grid.getValue(ijk.offsetBy(-1,0,0)), grid.getValue(ijk)); | |
| 909 | } | ||
| 910 | |||
| 911 | template<typename Accessor> | ||
| 912 | 5671060 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 913 | { | ||
| 914 | 5671060 | return difference(grid.getValue(ijk.offsetBy(0,-1,0)), grid.getValue(ijk)); | |
| 915 | } | ||
| 916 | |||
| 917 | template<typename Accessor> | ||
| 918 | 5671060 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 919 | { | ||
| 920 | 5671060 | return difference(grid.getValue(ijk.offsetBy(0, 0,-1)), grid.getValue(ijk)); | |
| 921 | } | ||
| 922 | |||
| 923 | |||
| 924 | // stencil access version | ||
| 925 | template<typename Stencil> | ||
| 926 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 927 | { | ||
| 928 | 93312 | return difference(S.template getValue<-1, 0, 0>(), S.template getValue< 0, 0, 0>()); | |
| 929 | } | ||
| 930 | |||
| 931 | template<typename Stencil> | ||
| 932 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 933 | { | ||
| 934 | 93312 | return difference(S.template getValue< 0,-1, 0>(), S.template getValue< 0, 0, 0>()); | |
| 935 | } | ||
| 936 | |||
| 937 | template<typename Stencil> | ||
| 938 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 939 | { | ||
| 940 | 93312 | return difference(S.template getValue< 0, 0,-1>(), S.template getValue< 0, 0, 0>()); | |
| 941 | } | ||
| 942 | }; | ||
| 943 | |||
| 944 | |||
| 945 | template<> | ||
| 946 | struct D1<BD_2ND> | ||
| 947 | { | ||
| 948 | |||
| 949 | // the difference opperator | ||
| 950 | template <typename ValueType> | ||
| 951 | 73728 | static ValueType difference(const ValueType& xm2, const ValueType& xm1, const ValueType& xm0) | |
| 952 | { | ||
| 953 | 73736 | return -D1<FD_2ND>::difference(xm2, xm1, xm0); | |
| 954 | } | ||
| 955 | |||
| 956 | |||
| 957 | // random access version | ||
| 958 | template<typename Accessor> | ||
| 959 | 12290 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 960 | { | ||
| 961 | 24580 | return difference( grid.getValue(ijk.offsetBy(-2,0,0)), | |
| 962 | 12290 | grid.getValue(ijk.offsetBy(-1,0,0)), | |
| 963 | 12290 | grid.getValue(ijk) ); | |
| 964 | } | ||
| 965 | |||
| 966 | template<typename Accessor> | ||
| 967 | 12290 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 968 | { | ||
| 969 | 24580 | return difference( grid.getValue(ijk.offsetBy(0,-2,0)), | |
| 970 | 12290 | grid.getValue(ijk.offsetBy(0,-1,0)), | |
| 971 | 12290 | grid.getValue(ijk) ); | |
| 972 | } | ||
| 973 | |||
| 974 | template<typename Accessor> | ||
| 975 | 12290 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 976 | { | ||
| 977 | 24580 | return difference( grid.getValue(ijk.offsetBy(0,0,-2)), | |
| 978 | 12290 | grid.getValue(ijk.offsetBy(0,0,-1)), | |
| 979 | 12290 | grid.getValue(ijk) ); | |
| 980 | } | ||
| 981 | |||
| 982 | // stencil access version | ||
| 983 | template<typename Stencil> | ||
| 984 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 985 | { | ||
| 986 | 12288 | return difference( S.template getValue<-2, 0, 0>(), | |
| 987 | S.template getValue<-1, 0, 0>(), | ||
| 988 | S.template getValue< 0, 0, 0>() ); | ||
| 989 | } | ||
| 990 | |||
| 991 | template<typename Stencil> | ||
| 992 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 993 | { | ||
| 994 | 12288 | return difference( S.template getValue< 0,-2, 0>(), | |
| 995 | S.template getValue< 0,-1, 0>(), | ||
| 996 | S.template getValue< 0, 0, 0>() ); | ||
| 997 | } | ||
| 998 | |||
| 999 | template<typename Stencil> | ||
| 1000 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 1001 | { | ||
| 1002 | 12288 | return difference( S.template getValue< 0, 0,-2>(), | |
| 1003 | S.template getValue< 0, 0,-1>(), | ||
| 1004 | S.template getValue< 0, 0, 0>() ); | ||
| 1005 | } | ||
| 1006 | }; | ||
| 1007 | |||
| 1008 | |||
| 1009 | template<> | ||
| 1010 | struct D1<BD_3RD> | ||
| 1011 | { | ||
| 1012 | |||
| 1013 | // the difference opperator | ||
| 1014 | template <typename ValueType> | ||
| 1015 | 49392 | static ValueType difference(const ValueType& xm3, const ValueType& xm2, | |
| 1016 | const ValueType& xm1, const ValueType& xm0) | ||
| 1017 | { | ||
| 1018 | 49400 | return -D1<FD_3RD>::difference(xm3, xm2, xm1, xm0); | |
| 1019 | } | ||
| 1020 | |||
| 1021 | // random access version | ||
| 1022 | template<typename Accessor> | ||
| 1023 | 8234 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 1024 | { | ||
| 1025 | 16468 | return difference( grid.getValue(ijk.offsetBy(-3,0,0)), | |
| 1026 | 8234 | grid.getValue(ijk.offsetBy(-2,0,0)), | |
| 1027 | 8234 | grid.getValue(ijk.offsetBy(-1,0,0)), | |
| 1028 | 8234 | grid.getValue(ijk) ); | |
| 1029 | } | ||
| 1030 | |||
| 1031 | template<typename Accessor> | ||
| 1032 | 8234 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 1033 | { | ||
| 1034 | 16468 | return difference( grid.getValue(ijk.offsetBy( 0,-3,0)), | |
| 1035 | 8234 | grid.getValue(ijk.offsetBy( 0,-2,0)), | |
| 1036 | 8234 | grid.getValue(ijk.offsetBy( 0,-1,0)), | |
| 1037 | 8234 | grid.getValue(ijk) ); | |
| 1038 | } | ||
| 1039 | |||
| 1040 | template<typename Accessor> | ||
| 1041 | 8234 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 1042 | { | ||
| 1043 | 16468 | return difference( grid.getValue(ijk.offsetBy( 0, 0,-3)), | |
| 1044 | 8234 | grid.getValue(ijk.offsetBy( 0, 0,-2)), | |
| 1045 | 8234 | grid.getValue(ijk.offsetBy( 0, 0,-1)), | |
| 1046 | 8234 | grid.getValue(ijk) ); | |
| 1047 | } | ||
| 1048 | |||
| 1049 | // stencil access version | ||
| 1050 | template<typename Stencil> | ||
| 1051 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 1052 | { | ||
| 1053 | 8232 | return difference( S.template getValue<-3, 0, 0>(), | |
| 1054 | S.template getValue<-2, 0, 0>(), | ||
| 1055 | S.template getValue<-1, 0, 0>(), | ||
| 1056 | S.template getValue< 0, 0, 0>() ); | ||
| 1057 | } | ||
| 1058 | |||
| 1059 | template<typename Stencil> | ||
| 1060 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 1061 | { | ||
| 1062 | 8232 | return difference( S.template getValue< 0,-3, 0>(), | |
| 1063 | S.template getValue< 0,-2, 0>(), | ||
| 1064 | S.template getValue< 0,-1, 0>(), | ||
| 1065 | S.template getValue< 0, 0, 0>() ); | ||
| 1066 | } | ||
| 1067 | |||
| 1068 | template<typename Stencil> | ||
| 1069 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 1070 | { | ||
| 1071 | 8232 | return difference( S.template getValue< 0, 0,-3>(), | |
| 1072 | S.template getValue< 0, 0,-2>(), | ||
| 1073 | S.template getValue< 0, 0,-1>(), | ||
| 1074 | S.template getValue< 0, 0, 0>() ); | ||
| 1075 | } | ||
| 1076 | |||
| 1077 | }; | ||
| 1078 | |||
| 1079 | template<> | ||
| 1080 | struct D1<FD_WENO5> | ||
| 1081 | { | ||
| 1082 | // the difference operator | ||
| 1083 | template <typename ValueType> | ||
| 1084 | 12 | static ValueType difference(const ValueType& xp3, const ValueType& xp2, | |
| 1085 | const ValueType& xp1, const ValueType& xp0, | ||
| 1086 | const ValueType& xm1, const ValueType& xm2) { | ||
| 1087 | 12 | return WENO5<ValueType>(xp3, xp2, xp1, xp0, xm1) | |
| 1088 | 12 | - WENO5<ValueType>(xp2, xp1, xp0, xm1, xm2); | |
| 1089 | } | ||
| 1090 | |||
| 1091 | |||
| 1092 | // random access version | ||
| 1093 | template<typename Accessor> | ||
| 1094 | 1 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 1095 | { | ||
| 1096 | using ValueType = typename Accessor::ValueType; | ||
| 1097 | ValueType V[6]; | ||
| 1098 | 1 | V[0] = grid.getValue(ijk.offsetBy(3,0,0)); | |
| 1099 | 1 | V[1] = grid.getValue(ijk.offsetBy(2,0,0)); | |
| 1100 | 1 | V[2] = grid.getValue(ijk.offsetBy(1,0,0)); | |
| 1101 | 1 | V[3] = grid.getValue(ijk); | |
| 1102 | 1 | V[4] = grid.getValue(ijk.offsetBy(-1,0,0)); | |
| 1103 | 1 | V[5] = grid.getValue(ijk.offsetBy(-2,0,0)); | |
| 1104 | |||
| 1105 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1106 | } | ||
| 1107 | |||
| 1108 | template<typename Accessor> | ||
| 1109 | 1 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 1110 | { | ||
| 1111 | using ValueType = typename Accessor::ValueType; | ||
| 1112 | ValueType V[6]; | ||
| 1113 | 1 | V[0] = grid.getValue(ijk.offsetBy(0,3,0)); | |
| 1114 | 1 | V[1] = grid.getValue(ijk.offsetBy(0,2,0)); | |
| 1115 | 1 | V[2] = grid.getValue(ijk.offsetBy(0,1,0)); | |
| 1116 | 1 | V[3] = grid.getValue(ijk); | |
| 1117 | 1 | V[4] = grid.getValue(ijk.offsetBy(0,-1,0)); | |
| 1118 | 1 | V[5] = grid.getValue(ijk.offsetBy(0,-2,0)); | |
| 1119 | |||
| 1120 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1121 | } | ||
| 1122 | |||
| 1123 | template<typename Accessor> | ||
| 1124 | 1 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 1125 | { | ||
| 1126 | using ValueType = typename Accessor::ValueType; | ||
| 1127 | ValueType V[6]; | ||
| 1128 | 1 | V[0] = grid.getValue(ijk.offsetBy(0,0,3)); | |
| 1129 | 1 | V[1] = grid.getValue(ijk.offsetBy(0,0,2)); | |
| 1130 | 1 | V[2] = grid.getValue(ijk.offsetBy(0,0,1)); | |
| 1131 | 1 | V[3] = grid.getValue(ijk); | |
| 1132 | 1 | V[4] = grid.getValue(ijk.offsetBy(0,0,-1)); | |
| 1133 | 1 | V[5] = grid.getValue(ijk.offsetBy(0,0,-2)); | |
| 1134 | |||
| 1135 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1136 | } | ||
| 1137 | |||
| 1138 | // stencil access version | ||
| 1139 | template<typename Stencil> | ||
| 1140 | 1 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 1141 | { | ||
| 1142 | |||
| 1143 | 1 | return static_cast<typename Stencil::ValueType>(difference( | |
| 1144 | S.template getValue< 3, 0, 0>(), | ||
| 1145 | S.template getValue< 2, 0, 0>(), | ||
| 1146 | S.template getValue< 1, 0, 0>(), | ||
| 1147 | S.template getValue< 0, 0, 0>(), | ||
| 1148 | S.template getValue<-1, 0, 0>(), | ||
| 1149 | 1 | S.template getValue<-2, 0, 0>() )); | |
| 1150 | |||
| 1151 | } | ||
| 1152 | |||
| 1153 | template<typename Stencil> | ||
| 1154 | 1 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 1155 | { | ||
| 1156 | 1 | return static_cast<typename Stencil::ValueType>(difference( | |
| 1157 | S.template getValue< 0, 3, 0>(), | ||
| 1158 | S.template getValue< 0, 2, 0>(), | ||
| 1159 | S.template getValue< 0, 1, 0>(), | ||
| 1160 | S.template getValue< 0, 0, 0>(), | ||
| 1161 | S.template getValue< 0,-1, 0>(), | ||
| 1162 | 1 | S.template getValue< 0,-2, 0>() )); | |
| 1163 | } | ||
| 1164 | |||
| 1165 | template<typename Stencil> | ||
| 1166 | 1 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 1167 | { | ||
| 1168 | 1 | return static_cast<typename Stencil::ValueType>(difference( | |
| 1169 | S.template getValue< 0, 0, 3>(), | ||
| 1170 | S.template getValue< 0, 0, 2>(), | ||
| 1171 | S.template getValue< 0, 0, 1>(), | ||
| 1172 | S.template getValue< 0, 0, 0>(), | ||
| 1173 | S.template getValue< 0, 0,-1>(), | ||
| 1174 | 1 | S.template getValue< 0, 0,-2>() )); | |
| 1175 | } | ||
| 1176 | }; | ||
| 1177 | |||
| 1178 | template<> | ||
| 1179 | struct D1<FD_HJWENO5> | ||
| 1180 | { | ||
| 1181 | |||
| 1182 | // the difference opperator | ||
| 1183 | template <typename ValueType> | ||
| 1184 | 14387652 | static ValueType difference(const ValueType& xp3, const ValueType& xp2, | |
| 1185 | const ValueType& xp1, const ValueType& xp0, | ||
| 1186 | const ValueType& xm1, const ValueType& xm2) { | ||
| 1187 | 14387652 | return WENO5<ValueType>(xp3 - xp2, xp2 - xp1, xp1 - xp0, xp0-xm1, xm1-xm2); | |
| 1188 | } | ||
| 1189 | |||
| 1190 | // random access version | ||
| 1191 | template<typename Accessor> | ||
| 1192 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | ||
| 1193 | { | ||
| 1194 | using ValueType = typename Accessor::ValueType; | ||
| 1195 | ValueType V[6]; | ||
| 1196 | V[0] = grid.getValue(ijk.offsetBy(3,0,0)); | ||
| 1197 | V[1] = grid.getValue(ijk.offsetBy(2,0,0)); | ||
| 1198 | V[2] = grid.getValue(ijk.offsetBy(1,0,0)); | ||
| 1199 | V[3] = grid.getValue(ijk); | ||
| 1200 | V[4] = grid.getValue(ijk.offsetBy(-1,0,0)); | ||
| 1201 | V[5] = grid.getValue(ijk.offsetBy(-2,0,0)); | ||
| 1202 | |||
| 1203 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1204 | |||
| 1205 | } | ||
| 1206 | |||
| 1207 | template<typename Accessor> | ||
| 1208 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | ||
| 1209 | { | ||
| 1210 | using ValueType = typename Accessor::ValueType; | ||
| 1211 | ValueType V[6]; | ||
| 1212 | V[0] = grid.getValue(ijk.offsetBy(0,3,0)); | ||
| 1213 | V[1] = grid.getValue(ijk.offsetBy(0,2,0)); | ||
| 1214 | V[2] = grid.getValue(ijk.offsetBy(0,1,0)); | ||
| 1215 | V[3] = grid.getValue(ijk); | ||
| 1216 | V[4] = grid.getValue(ijk.offsetBy(0,-1,0)); | ||
| 1217 | V[5] = grid.getValue(ijk.offsetBy(0,-2,0)); | ||
| 1218 | |||
| 1219 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1220 | } | ||
| 1221 | |||
| 1222 | template<typename Accessor> | ||
| 1223 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | ||
| 1224 | { | ||
| 1225 | using ValueType = typename Accessor::ValueType; | ||
| 1226 | ValueType V[6]; | ||
| 1227 | V[0] = grid.getValue(ijk.offsetBy(0,0,3)); | ||
| 1228 | V[1] = grid.getValue(ijk.offsetBy(0,0,2)); | ||
| 1229 | V[2] = grid.getValue(ijk.offsetBy(0,0,1)); | ||
| 1230 | V[3] = grid.getValue(ijk); | ||
| 1231 | V[4] = grid.getValue(ijk.offsetBy(0,0,-1)); | ||
| 1232 | V[5] = grid.getValue(ijk.offsetBy(0,0,-2)); | ||
| 1233 | |||
| 1234 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1235 | } | ||
| 1236 | |||
| 1237 | // stencil access version | ||
| 1238 | template<typename Stencil> | ||
| 1239 | 2397942 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 1240 | { | ||
| 1241 | |||
| 1242 | 2397942 | return difference( S.template getValue< 3, 0, 0>(), | |
| 1243 | S.template getValue< 2, 0, 0>(), | ||
| 1244 | S.template getValue< 1, 0, 0>(), | ||
| 1245 | S.template getValue< 0, 0, 0>(), | ||
| 1246 | S.template getValue<-1, 0, 0>(), | ||
| 1247 | 2397942 | S.template getValue<-2, 0, 0>() ); | |
| 1248 | |||
| 1249 | } | ||
| 1250 | |||
| 1251 | template<typename Stencil> | ||
| 1252 | 2397942 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 1253 | { | ||
| 1254 | 2397942 | return difference( S.template getValue< 0, 3, 0>(), | |
| 1255 | S.template getValue< 0, 2, 0>(), | ||
| 1256 | S.template getValue< 0, 1, 0>(), | ||
| 1257 | S.template getValue< 0, 0, 0>(), | ||
| 1258 | S.template getValue< 0,-1, 0>(), | ||
| 1259 | 2397942 | S.template getValue< 0,-2, 0>() ); | |
| 1260 | } | ||
| 1261 | |||
| 1262 | template<typename Stencil> | ||
| 1263 | 2397942 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 1264 | { | ||
| 1265 | |||
| 1266 | 2397942 | return difference( S.template getValue< 0, 0, 3>(), | |
| 1267 | S.template getValue< 0, 0, 2>(), | ||
| 1268 | S.template getValue< 0, 0, 1>(), | ||
| 1269 | S.template getValue< 0, 0, 0>(), | ||
| 1270 | S.template getValue< 0, 0,-1>(), | ||
| 1271 | 2397942 | S.template getValue< 0, 0,-2>() ); | |
| 1272 | } | ||
| 1273 | |||
| 1274 | }; | ||
| 1275 | |||
| 1276 | template<> | ||
| 1277 | struct D1<BD_WENO5> | ||
| 1278 | { | ||
| 1279 | |||
| 1280 | template<typename ValueType> | ||
| 1281 | static ValueType difference(const ValueType& xm3, const ValueType& xm2, const ValueType& xm1, | ||
| 1282 | const ValueType& xm0, const ValueType& xp1, const ValueType& xp2) | ||
| 1283 | { | ||
| 1284 | 6 | return -D1<FD_WENO5>::difference(xm3, xm2, xm1, xm0, xp1, xp2); | |
| 1285 | } | ||
| 1286 | |||
| 1287 | |||
| 1288 | // random access version | ||
| 1289 | template<typename Accessor> | ||
| 1290 | 1 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 1291 | { | ||
| 1292 | using ValueType = typename Accessor::ValueType; | ||
| 1293 | ValueType V[6]; | ||
| 1294 | 1 | V[0] = grid.getValue(ijk.offsetBy(-3,0,0)); | |
| 1295 | 1 | V[1] = grid.getValue(ijk.offsetBy(-2,0,0)); | |
| 1296 | 1 | V[2] = grid.getValue(ijk.offsetBy(-1,0,0)); | |
| 1297 | 1 | V[3] = grid.getValue(ijk); | |
| 1298 | 1 | V[4] = grid.getValue(ijk.offsetBy(1,0,0)); | |
| 1299 | 1 | V[5] = grid.getValue(ijk.offsetBy(2,0,0)); | |
| 1300 | |||
| 1301 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1302 | } | ||
| 1303 | |||
| 1304 | template<typename Accessor> | ||
| 1305 | 1 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 1306 | { | ||
| 1307 | using ValueType = typename Accessor::ValueType; | ||
| 1308 | ValueType V[6]; | ||
| 1309 | 1 | V[0] = grid.getValue(ijk.offsetBy(0,-3,0)); | |
| 1310 | 1 | V[1] = grid.getValue(ijk.offsetBy(0,-2,0)); | |
| 1311 | 1 | V[2] = grid.getValue(ijk.offsetBy(0,-1,0)); | |
| 1312 | 1 | V[3] = grid.getValue(ijk); | |
| 1313 | 1 | V[4] = grid.getValue(ijk.offsetBy(0,1,0)); | |
| 1314 | 1 | V[5] = grid.getValue(ijk.offsetBy(0,2,0)); | |
| 1315 | |||
| 1316 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1317 | } | ||
| 1318 | |||
| 1319 | template<typename Accessor> | ||
| 1320 | 1 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 1321 | { | ||
| 1322 | using ValueType = typename Accessor::ValueType; | ||
| 1323 | ValueType V[6]; | ||
| 1324 | 1 | V[0] = grid.getValue(ijk.offsetBy(0,0,-3)); | |
| 1325 | 1 | V[1] = grid.getValue(ijk.offsetBy(0,0,-2)); | |
| 1326 | 1 | V[2] = grid.getValue(ijk.offsetBy(0,0,-1)); | |
| 1327 | 1 | V[3] = grid.getValue(ijk); | |
| 1328 | 1 | V[4] = grid.getValue(ijk.offsetBy(0,0,1)); | |
| 1329 | 1 | V[5] = grid.getValue(ijk.offsetBy(0,0,2)); | |
| 1330 | |||
| 1331 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1332 | } | ||
| 1333 | |||
| 1334 | // stencil access version | ||
| 1335 | template<typename Stencil> | ||
| 1336 | 1 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 1337 | { | ||
| 1338 | using ValueType = typename Stencil::ValueType; | ||
| 1339 | ValueType V[6]; | ||
| 1340 | 1 | V[0] = S.template getValue<-3, 0, 0>(); | |
| 1341 | 1 | V[1] = S.template getValue<-2, 0, 0>(); | |
| 1342 | 1 | V[2] = S.template getValue<-1, 0, 0>(); | |
| 1343 | 1 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1344 | 1 | V[4] = S.template getValue< 1, 0, 0>(); | |
| 1345 | 1 | V[5] = S.template getValue< 2, 0, 0>(); | |
| 1346 | |||
| 1347 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1348 | } | ||
| 1349 | |||
| 1350 | template<typename Stencil> | ||
| 1351 | 1 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 1352 | { | ||
| 1353 | using ValueType = typename Stencil::ValueType; | ||
| 1354 | ValueType V[6]; | ||
| 1355 | 1 | V[0] = S.template getValue< 0,-3, 0>(); | |
| 1356 | 1 | V[1] = S.template getValue< 0,-2, 0>(); | |
| 1357 | 1 | V[2] = S.template getValue< 0,-1, 0>(); | |
| 1358 | 1 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1359 | 1 | V[4] = S.template getValue< 0, 1, 0>(); | |
| 1360 | 1 | V[5] = S.template getValue< 0, 2, 0>(); | |
| 1361 | |||
| 1362 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1363 | } | ||
| 1364 | |||
| 1365 | template<typename Stencil> | ||
| 1366 | 1 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 1367 | { | ||
| 1368 | using ValueType = typename Stencil::ValueType; | ||
| 1369 | ValueType V[6]; | ||
| 1370 | 1 | V[0] = S.template getValue< 0, 0,-3>(); | |
| 1371 | 1 | V[1] = S.template getValue< 0, 0,-2>(); | |
| 1372 | 1 | V[2] = S.template getValue< 0, 0,-1>(); | |
| 1373 | 1 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1374 | 1 | V[4] = S.template getValue< 0, 0, 1>(); | |
| 1375 | 1 | V[5] = S.template getValue< 0, 0, 2>(); | |
| 1376 | |||
| 1377 | 1 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1378 | } | ||
| 1379 | }; | ||
| 1380 | |||
| 1381 | |||
| 1382 | template<> | ||
| 1383 | struct D1<BD_HJWENO5> | ||
| 1384 | { | ||
| 1385 | template<typename ValueType> | ||
| 1386 | static ValueType difference(const ValueType& xm3, const ValueType& xm2, const ValueType& xm1, | ||
| 1387 | const ValueType& xm0, const ValueType& xp1, const ValueType& xp2) | ||
| 1388 | { | ||
| 1389 | 7193826 | return -D1<FD_HJWENO5>::difference(xm3, xm2, xm1, xm0, xp1, xp2); | |
| 1390 | } | ||
| 1391 | |||
| 1392 | // random access version | ||
| 1393 | template<typename Accessor> | ||
| 1394 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | ||
| 1395 | { | ||
| 1396 | using ValueType = typename Accessor::ValueType; | ||
| 1397 | ValueType V[6]; | ||
| 1398 | V[0] = grid.getValue(ijk.offsetBy(-3,0,0)); | ||
| 1399 | V[1] = grid.getValue(ijk.offsetBy(-2,0,0)); | ||
| 1400 | V[2] = grid.getValue(ijk.offsetBy(-1,0,0)); | ||
| 1401 | V[3] = grid.getValue(ijk); | ||
| 1402 | V[4] = grid.getValue(ijk.offsetBy(1,0,0)); | ||
| 1403 | V[5] = grid.getValue(ijk.offsetBy(2,0,0)); | ||
| 1404 | |||
| 1405 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1406 | } | ||
| 1407 | |||
| 1408 | template<typename Accessor> | ||
| 1409 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | ||
| 1410 | { | ||
| 1411 | using ValueType = typename Accessor::ValueType; | ||
| 1412 | ValueType V[6]; | ||
| 1413 | V[0] = grid.getValue(ijk.offsetBy(0,-3,0)); | ||
| 1414 | V[1] = grid.getValue(ijk.offsetBy(0,-2,0)); | ||
| 1415 | V[2] = grid.getValue(ijk.offsetBy(0,-1,0)); | ||
| 1416 | V[3] = grid.getValue(ijk); | ||
| 1417 | V[4] = grid.getValue(ijk.offsetBy(0,1,0)); | ||
| 1418 | V[5] = grid.getValue(ijk.offsetBy(0,2,0)); | ||
| 1419 | |||
| 1420 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1421 | } | ||
| 1422 | |||
| 1423 | template<typename Accessor> | ||
| 1424 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | ||
| 1425 | { | ||
| 1426 | using ValueType = typename Accessor::ValueType; | ||
| 1427 | ValueType V[6]; | ||
| 1428 | V[0] = grid.getValue(ijk.offsetBy(0,0,-3)); | ||
| 1429 | V[1] = grid.getValue(ijk.offsetBy(0,0,-2)); | ||
| 1430 | V[2] = grid.getValue(ijk.offsetBy(0,0,-1)); | ||
| 1431 | V[3] = grid.getValue(ijk); | ||
| 1432 | V[4] = grid.getValue(ijk.offsetBy(0,0,1)); | ||
| 1433 | V[5] = grid.getValue(ijk.offsetBy(0,0,2)); | ||
| 1434 | |||
| 1435 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | ||
| 1436 | } | ||
| 1437 | |||
| 1438 | // stencil access version | ||
| 1439 | template<typename Stencil> | ||
| 1440 | 2397942 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 1441 | { | ||
| 1442 | using ValueType = typename Stencil::ValueType; | ||
| 1443 | ValueType V[6]; | ||
| 1444 | 2397942 | V[0] = S.template getValue<-3, 0, 0>(); | |
| 1445 | 2397942 | V[1] = S.template getValue<-2, 0, 0>(); | |
| 1446 | 2397942 | V[2] = S.template getValue<-1, 0, 0>(); | |
| 1447 | 2397942 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1448 | 2397942 | V[4] = S.template getValue< 1, 0, 0>(); | |
| 1449 | 2397942 | V[5] = S.template getValue< 2, 0, 0>(); | |
| 1450 | |||
| 1451 | 2397942 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1452 | } | ||
| 1453 | |||
| 1454 | template<typename Stencil> | ||
| 1455 | 2397942 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 1456 | { | ||
| 1457 | using ValueType = typename Stencil::ValueType; | ||
| 1458 | ValueType V[6]; | ||
| 1459 | 2397942 | V[0] = S.template getValue< 0,-3, 0>(); | |
| 1460 | 2397942 | V[1] = S.template getValue< 0,-2, 0>(); | |
| 1461 | 2397942 | V[2] = S.template getValue< 0,-1, 0>(); | |
| 1462 | 2397942 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1463 | 2397942 | V[4] = S.template getValue< 0, 1, 0>(); | |
| 1464 | 2397942 | V[5] = S.template getValue< 0, 2, 0>(); | |
| 1465 | |||
| 1466 | 2397942 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1467 | } | ||
| 1468 | |||
| 1469 | template<typename Stencil> | ||
| 1470 | 2397942 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 1471 | { | ||
| 1472 | using ValueType = typename Stencil::ValueType; | ||
| 1473 | ValueType V[6]; | ||
| 1474 | 2397942 | V[0] = S.template getValue< 0, 0,-3>(); | |
| 1475 | 2397942 | V[1] = S.template getValue< 0, 0,-2>(); | |
| 1476 | 2397942 | V[2] = S.template getValue< 0, 0,-1>(); | |
| 1477 | 2397942 | V[3] = S.template getValue< 0, 0, 0>(); | |
| 1478 | 2397942 | V[4] = S.template getValue< 0, 0, 1>(); | |
| 1479 | 2397942 | V[5] = S.template getValue< 0, 0, 2>(); | |
| 1480 | |||
| 1481 | 2397942 | return difference(V[0], V[1], V[2], V[3], V[4], V[5]); | |
| 1482 | } | ||
| 1483 | }; | ||
| 1484 | |||
| 1485 | |||
| 1486 | template<DScheme DiffScheme> | ||
| 1487 | struct D1Vec | ||
| 1488 | { | ||
| 1489 | // random access version | ||
| 1490 | template<typename Accessor> | ||
| 1491 | static typename Accessor::ValueType::value_type | ||
| 1492 | 26371910 | inX(const Accessor& grid, const Coord& ijk, int n) | |
| 1493 | { | ||
| 1494 | 26371910 | return D1<DiffScheme>::inX(grid, ijk)[n]; | |
| 1495 | } | ||
| 1496 | |||
| 1497 | template<typename Accessor> | ||
| 1498 | static typename Accessor::ValueType::value_type | ||
| 1499 | 26371910 | inY(const Accessor& grid, const Coord& ijk, int n) | |
| 1500 | { | ||
| 1501 | 26371910 | return D1<DiffScheme>::inY(grid, ijk)[n]; | |
| 1502 | } | ||
| 1503 | template<typename Accessor> | ||
| 1504 | static typename Accessor::ValueType::value_type | ||
| 1505 | 26371910 | inZ(const Accessor& grid, const Coord& ijk, int n) | |
| 1506 | { | ||
| 1507 | 26371910 | return D1<DiffScheme>::inZ(grid, ijk)[n]; | |
| 1508 | } | ||
| 1509 | |||
| 1510 | |||
| 1511 | // stencil access version | ||
| 1512 | template<typename Stencil> | ||
| 1513 |
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455328 | static typename Stencil::ValueType::value_type inX(const Stencil& S, int n) |
| 1514 | { | ||
| 1515 |
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455328 | return D1<DiffScheme>::inX(S)[n]; |
| 1516 | } | ||
| 1517 | |||
| 1518 | template<typename Stencil> | ||
| 1519 |
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455328 | static typename Stencil::ValueType::value_type inY(const Stencil& S, int n) |
| 1520 | { | ||
| 1521 |
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455328 | return D1<DiffScheme>::inY(S)[n]; |
| 1522 | } | ||
| 1523 | |||
| 1524 | template<typename Stencil> | ||
| 1525 |
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455328 | static typename Stencil::ValueType::value_type inZ(const Stencil& S, int n) |
| 1526 | { | ||
| 1527 |
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455328 | return D1<DiffScheme>::inZ(S)[n]; |
| 1528 | } | ||
| 1529 | }; | ||
| 1530 | |||
| 1531 | |||
| 1532 | template<> | ||
| 1533 | struct D1Vec<CD_2NDT> | ||
| 1534 | { | ||
| 1535 | |||
| 1536 | // random access version | ||
| 1537 | template<typename Accessor> | ||
| 1538 | static typename Accessor::ValueType::value_type | ||
| 1539 | 2273338 | inX(const Accessor& grid, const Coord& ijk, int n) | |
| 1540 | { | ||
| 1541 | 2273338 | return D1<CD_2NDT>::difference( grid.getValue(ijk.offsetBy( 1, 0, 0))[n], | |
| 1542 | 2273338 | grid.getValue(ijk.offsetBy(-1, 0, 0))[n] ); | |
| 1543 | } | ||
| 1544 | |||
| 1545 | template<typename Accessor> | ||
| 1546 | static typename Accessor::ValueType::value_type | ||
| 1547 | 2273338 | inY(const Accessor& grid, const Coord& ijk, int n) | |
| 1548 | { | ||
| 1549 | 2273338 | return D1<CD_2NDT>::difference( grid.getValue(ijk.offsetBy(0, 1, 0))[n], | |
| 1550 | 2273338 | grid.getValue(ijk.offsetBy(0,-1, 0))[n] ); | |
| 1551 | } | ||
| 1552 | |||
| 1553 | template<typename Accessor> | ||
| 1554 | static typename Accessor::ValueType::value_type | ||
| 1555 | 2273338 | inZ(const Accessor& grid, const Coord& ijk, int n) | |
| 1556 | { | ||
| 1557 | 2273338 | return D1<CD_2NDT>::difference( grid.getValue(ijk.offsetBy(0, 0, 1))[n], | |
| 1558 | 2273338 | grid.getValue(ijk.offsetBy(0, 0,-1))[n] ); | |
| 1559 | } | ||
| 1560 | |||
| 1561 | // stencil access version | ||
| 1562 | template<typename Stencil> | ||
| 1563 | static typename Stencil::ValueType::value_type inX(const Stencil& S, int n) | ||
| 1564 | { | ||
| 1565 | return D1<CD_2NDT>::difference( S.template getValue< 1, 0, 0>()[n], | ||
| 1566 | S.template getValue<-1, 0, 0>()[n] ); | ||
| 1567 | } | ||
| 1568 | |||
| 1569 | template<typename Stencil> | ||
| 1570 | static typename Stencil::ValueType::value_type inY(const Stencil& S, int n) | ||
| 1571 | { | ||
| 1572 | return D1<CD_2NDT>::difference( S.template getValue< 0, 1, 0>()[n], | ||
| 1573 | S.template getValue< 0,-1, 0>()[n] ); | ||
| 1574 | } | ||
| 1575 | |||
| 1576 | template<typename Stencil> | ||
| 1577 | static typename Stencil::ValueType::value_type inZ(const Stencil& S, int n) | ||
| 1578 | { | ||
| 1579 | return D1<CD_2NDT>::difference( S.template getValue< 0, 0, 1>()[n], | ||
| 1580 | S.template getValue< 0, 0,-1>()[n] ); | ||
| 1581 | } | ||
| 1582 | }; | ||
| 1583 | |||
| 1584 | template<> | ||
| 1585 | struct D1Vec<CD_2ND> | ||
| 1586 | { | ||
| 1587 | |||
| 1588 | // random access version | ||
| 1589 | template<typename Accessor> | ||
| 1590 | static typename Accessor::ValueType::value_type | ||
| 1591 | 99144 | inX(const Accessor& grid, const Coord& ijk, int n) | |
| 1592 | { | ||
| 1593 | 99144 | return D1<CD_2ND>::difference( grid.getValue(ijk.offsetBy( 1, 0, 0))[n] , | |
| 1594 | 99144 | grid.getValue(ijk.offsetBy(-1, 0, 0))[n] ); | |
| 1595 | } | ||
| 1596 | |||
| 1597 | template<typename Accessor> | ||
| 1598 | static typename Accessor::ValueType::value_type | ||
| 1599 | 99144 | inY(const Accessor& grid, const Coord& ijk, int n) | |
| 1600 | { | ||
| 1601 | 99144 | return D1<CD_2ND>::difference( grid.getValue(ijk.offsetBy(0, 1, 0))[n] , | |
| 1602 | 99144 | grid.getValue(ijk.offsetBy(0,-1, 0))[n] ); | |
| 1603 | } | ||
| 1604 | |||
| 1605 | template<typename Accessor> | ||
| 1606 | static typename Accessor::ValueType::value_type | ||
| 1607 | 99144 | inZ(const Accessor& grid, const Coord& ijk, int n) | |
| 1608 | { | ||
| 1609 | 99144 | return D1<CD_2ND>::difference( grid.getValue(ijk.offsetBy(0, 0, 1))[n] , | |
| 1610 | 99144 | grid.getValue(ijk.offsetBy(0, 0,-1))[n] ); | |
| 1611 | } | ||
| 1612 | |||
| 1613 | |||
| 1614 | // stencil access version | ||
| 1615 | template<typename Stencil> | ||
| 1616 |
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52488 | static typename Stencil::ValueType::value_type inX(const Stencil& S, int n) |
| 1617 | { | ||
| 1618 | return D1<CD_2ND>::difference( S.template getValue< 1, 0, 0>()[n], | ||
| 1619 | 52488 | S.template getValue<-1, 0, 0>()[n] ); | |
| 1620 | } | ||
| 1621 | |||
| 1622 | template<typename Stencil> | ||
| 1623 |
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52488 | static typename Stencil::ValueType::value_type inY(const Stencil& S, int n) |
| 1624 | { | ||
| 1625 | return D1<CD_2ND>::difference( S.template getValue< 0, 1, 0>()[n], | ||
| 1626 | 52488 | S.template getValue< 0,-1, 0>()[n] ); | |
| 1627 | } | ||
| 1628 | |||
| 1629 | template<typename Stencil> | ||
| 1630 |
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52488 | static typename Stencil::ValueType::value_type inZ(const Stencil& S, int n) |
| 1631 | { | ||
| 1632 | return D1<CD_2ND>::difference( S.template getValue< 0, 0, 1>()[n], | ||
| 1633 | 52488 | S.template getValue< 0, 0,-1>()[n] ); | |
| 1634 | } | ||
| 1635 | }; | ||
| 1636 | |||
| 1637 | |||
| 1638 | template<> | ||
| 1639 | struct D1Vec<CD_4TH> { | ||
| 1640 | // using value_type = typename Accessor::ValueType::value_type; | ||
| 1641 | |||
| 1642 | |||
| 1643 | // random access version | ||
| 1644 | template<typename Accessor> | ||
| 1645 | static typename Accessor::ValueType::value_type | ||
| 1646 | 12288 | inX(const Accessor& grid, const Coord& ijk, int n) | |
| 1647 | { | ||
| 1648 | return D1<CD_4TH>::difference( | ||
| 1649 |
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12288 | grid.getValue(ijk.offsetBy(2, 0, 0))[n], grid.getValue(ijk.offsetBy( 1, 0, 0))[n], |
| 1650 |
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36864 | grid.getValue(ijk.offsetBy(-1,0, 0))[n], grid.getValue(ijk.offsetBy(-2, 0, 0))[n]); |
| 1651 | } | ||
| 1652 | |||
| 1653 | template<typename Accessor> | ||
| 1654 | static typename Accessor::ValueType::value_type | ||
| 1655 | 12288 | inY(const Accessor& grid, const Coord& ijk, int n) | |
| 1656 | { | ||
| 1657 | return D1<CD_4TH>::difference( | ||
| 1658 |
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12288 | grid.getValue(ijk.offsetBy( 0, 2, 0))[n], grid.getValue(ijk.offsetBy( 0, 1, 0))[n], |
| 1659 |
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36864 | grid.getValue(ijk.offsetBy( 0,-1, 0))[n], grid.getValue(ijk.offsetBy( 0,-2, 0))[n]); |
| 1660 | } | ||
| 1661 | |||
| 1662 | template<typename Accessor> | ||
| 1663 | static typename Accessor::ValueType::value_type | ||
| 1664 | 12288 | inZ(const Accessor& grid, const Coord& ijk, int n) | |
| 1665 | { | ||
| 1666 | return D1<CD_4TH>::difference( | ||
| 1667 |
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12288 | grid.getValue(ijk.offsetBy(0,0, 2))[n], grid.getValue(ijk.offsetBy( 0, 0, 1))[n], |
| 1668 |
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36864 | grid.getValue(ijk.offsetBy(0,0,-1))[n], grid.getValue(ijk.offsetBy( 0, 0,-2))[n]); |
| 1669 | } | ||
| 1670 | |||
| 1671 | // stencil access version | ||
| 1672 | template<typename Stencil> | ||
| 1673 |
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12288 | static typename Stencil::ValueType::value_type inX(const Stencil& S, int n) |
| 1674 | { | ||
| 1675 | return D1<CD_4TH>::difference( | ||
| 1676 | S.template getValue< 2, 0, 0>()[n], S.template getValue< 1, 0, 0>()[n], | ||
| 1677 | 12288 | S.template getValue<-1, 0, 0>()[n], S.template getValue<-2, 0, 0>()[n] ); | |
| 1678 | } | ||
| 1679 | |||
| 1680 | template<typename Stencil> | ||
| 1681 |
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12288 | static typename Stencil::ValueType::value_type inY(const Stencil& S, int n) |
| 1682 | { | ||
| 1683 | return D1<CD_4TH>::difference( | ||
| 1684 | S.template getValue< 0, 2, 0>()[n], S.template getValue< 0, 1, 0>()[n], | ||
| 1685 | 12288 | S.template getValue< 0,-1, 0>()[n], S.template getValue< 0,-2, 0>()[n]); | |
| 1686 | } | ||
| 1687 | |||
| 1688 | template<typename Stencil> | ||
| 1689 |
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12288 | static typename Stencil::ValueType::value_type inZ(const Stencil& S, int n) |
| 1690 | { | ||
| 1691 | return D1<CD_4TH>::difference( | ||
| 1692 | S.template getValue< 0, 0, 2>()[n], S.template getValue< 0, 0, 1>()[n], | ||
| 1693 | 12288 | S.template getValue< 0, 0,-1>()[n], S.template getValue< 0, 0,-2>()[n]); | |
| 1694 | } | ||
| 1695 | }; | ||
| 1696 | |||
| 1697 | |||
| 1698 | template<> | ||
| 1699 | struct D1Vec<CD_6TH> | ||
| 1700 | { | ||
| 1701 | //using ValueType = typename Accessor::ValueType::value_type::value_type; | ||
| 1702 | |||
| 1703 | // random access version | ||
| 1704 | template<typename Accessor> | ||
| 1705 | static typename Accessor::ValueType::value_type | ||
| 1706 | 8232 | inX(const Accessor& grid, const Coord& ijk, int n) | |
| 1707 | { | ||
| 1708 | return D1<CD_6TH>::difference( | ||
| 1709 |
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8232 | grid.getValue(ijk.offsetBy( 3, 0, 0))[n], grid.getValue(ijk.offsetBy( 2, 0, 0))[n], |
| 1710 |
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8232 | grid.getValue(ijk.offsetBy( 1, 0, 0))[n], grid.getValue(ijk.offsetBy(-1, 0, 0))[n], |
| 1711 |
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24696 | grid.getValue(ijk.offsetBy(-2, 0, 0))[n], grid.getValue(ijk.offsetBy(-3, 0, 0))[n] ); |
| 1712 | } | ||
| 1713 | |||
| 1714 | template<typename Accessor> | ||
| 1715 | static typename Accessor::ValueType::value_type | ||
| 1716 | 8232 | inY(const Accessor& grid, const Coord& ijk, int n) | |
| 1717 | { | ||
| 1718 | return D1<CD_6TH>::difference( | ||
| 1719 |
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8232 | grid.getValue(ijk.offsetBy( 0, 3, 0))[n], grid.getValue(ijk.offsetBy( 0, 2, 0))[n], |
| 1720 |
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8232 | grid.getValue(ijk.offsetBy( 0, 1, 0))[n], grid.getValue(ijk.offsetBy( 0,-1, 0))[n], |
| 1721 |
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24696 | grid.getValue(ijk.offsetBy( 0,-2, 0))[n], grid.getValue(ijk.offsetBy( 0,-3, 0))[n] ); |
| 1722 | } | ||
| 1723 | |||
| 1724 | template<typename Accessor> | ||
| 1725 | static typename Accessor::ValueType::value_type | ||
| 1726 | 8232 | inZ(const Accessor& grid, const Coord& ijk, int n) | |
| 1727 | { | ||
| 1728 | return D1<CD_6TH>::difference( | ||
| 1729 |
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8232 | grid.getValue(ijk.offsetBy( 0, 0, 3))[n], grid.getValue(ijk.offsetBy( 0, 0, 2))[n], |
| 1730 |
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8232 | grid.getValue(ijk.offsetBy( 0, 0, 1))[n], grid.getValue(ijk.offsetBy( 0, 0,-1))[n], |
| 1731 |
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24696 | grid.getValue(ijk.offsetBy( 0, 0,-2))[n], grid.getValue(ijk.offsetBy( 0, 0,-3))[n] ); |
| 1732 | } | ||
| 1733 | |||
| 1734 | |||
| 1735 | // stencil access version | ||
| 1736 | template<typename Stencil> | ||
| 1737 |
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8232 | static typename Stencil::ValueType::value_type inX(const Stencil& S, int n) |
| 1738 | { | ||
| 1739 | return D1<CD_6TH>::difference( | ||
| 1740 | S.template getValue< 3, 0, 0>()[n], S.template getValue< 2, 0, 0>()[n], | ||
| 1741 | S.template getValue< 1, 0, 0>()[n], S.template getValue<-1, 0, 0>()[n], | ||
| 1742 | 8232 | S.template getValue<-2, 0, 0>()[n], S.template getValue<-3, 0, 0>()[n] ); | |
| 1743 | } | ||
| 1744 | |||
| 1745 | template<typename Stencil> | ||
| 1746 |
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8232 | static typename Stencil::ValueType::value_type inY(const Stencil& S, int n) |
| 1747 | { | ||
| 1748 | return D1<CD_6TH>::difference( | ||
| 1749 | S.template getValue< 0, 3, 0>()[n], S.template getValue< 0, 2, 0>()[n], | ||
| 1750 | S.template getValue< 0, 1, 0>()[n], S.template getValue< 0,-1, 0>()[n], | ||
| 1751 | 8232 | S.template getValue< 0,-2, 0>()[n], S.template getValue< 0,-3, 0>()[n] ); | |
| 1752 | } | ||
| 1753 | |||
| 1754 | template<typename Stencil> | ||
| 1755 |
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8232 | static typename Stencil::ValueType::value_type inZ(const Stencil& S, int n) |
| 1756 | { | ||
| 1757 | return D1<CD_6TH>::difference( | ||
| 1758 | S.template getValue< 0, 0, 3>()[n], S.template getValue< 0, 0, 2>()[n], | ||
| 1759 | S.template getValue< 0, 0, 1>()[n], S.template getValue< 0, 0,-1>()[n], | ||
| 1760 | 8232 | S.template getValue< 0, 0,-2>()[n], S.template getValue< 0, 0,-3>()[n] ); | |
| 1761 | } | ||
| 1762 | }; | ||
| 1763 | |||
| 1764 | template<DDScheme DiffScheme> | ||
| 1765 | struct D2 | ||
| 1766 | { | ||
| 1767 | |||
| 1768 | template<typename Accessor> | ||
| 1769 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk); | ||
| 1770 | template<typename Accessor> | ||
| 1771 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk); | ||
| 1772 | template<typename Accessor> | ||
| 1773 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk); | ||
| 1774 | |||
| 1775 | // cross derivatives | ||
| 1776 | template<typename Accessor> | ||
| 1777 | static typename Accessor::ValueType inXandY(const Accessor& grid, const Coord& ijk); | ||
| 1778 | |||
| 1779 | template<typename Accessor> | ||
| 1780 | static typename Accessor::ValueType inXandZ(const Accessor& grid, const Coord& ijk); | ||
| 1781 | |||
| 1782 | template<typename Accessor> | ||
| 1783 | static typename Accessor::ValueType inYandZ(const Accessor& grid, const Coord& ijk); | ||
| 1784 | |||
| 1785 | |||
| 1786 | // stencil access version | ||
| 1787 | template<typename Stencil> | ||
| 1788 | static typename Stencil::ValueType inX(const Stencil& S); | ||
| 1789 | template<typename Stencil> | ||
| 1790 | static typename Stencil::ValueType inY(const Stencil& S); | ||
| 1791 | template<typename Stencil> | ||
| 1792 | static typename Stencil::ValueType inZ(const Stencil& S); | ||
| 1793 | |||
| 1794 | // cross derivatives | ||
| 1795 | template<typename Stencil> | ||
| 1796 | static typename Stencil::ValueType inXandY(const Stencil& S); | ||
| 1797 | |||
| 1798 | template<typename Stencil> | ||
| 1799 | static typename Stencil::ValueType inXandZ(const Stencil& S); | ||
| 1800 | |||
| 1801 | template<typename Stencil> | ||
| 1802 | static typename Stencil::ValueType inYandZ(const Stencil& S); | ||
| 1803 | }; | ||
| 1804 | |||
| 1805 | template<> | ||
| 1806 | struct D2<CD_SECOND> | ||
| 1807 | { | ||
| 1808 | |||
| 1809 | // the difference opperator | ||
| 1810 | template <typename ValueType> | ||
| 1811 | static ValueType difference(const ValueType& xp1, const ValueType& xp0, const ValueType& xm1) | ||
| 1812 | { | ||
| 1813 | 789501 | return xp1 + xm1 - ValueType(2)*xp0; | |
| 1814 | } | ||
| 1815 | |||
| 1816 | template <typename ValueType> | ||
| 1817 | static ValueType crossdifference(const ValueType& xpyp, const ValueType& xpym, | ||
| 1818 | const ValueType& xmyp, const ValueType& xmym) | ||
| 1819 | { | ||
| 1820 | 789462 | return ValueType(0.25)*(xpyp + xmym - xpym - xmyp); | |
| 1821 | } | ||
| 1822 | |||
| 1823 | // random access version | ||
| 1824 | template<typename Accessor> | ||
| 1825 | 526318 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 1826 | { | ||
| 1827 | 526318 | return difference( grid.getValue(ijk.offsetBy( 1,0,0)), grid.getValue(ijk), | |
| 1828 | 526318 | grid.getValue(ijk.offsetBy(-1,0,0)) ); | |
| 1829 | } | ||
| 1830 | |||
| 1831 | template<typename Accessor> | ||
| 1832 | 526318 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 1833 | { | ||
| 1834 | |||
| 1835 | 526318 | return difference( grid.getValue(ijk.offsetBy(0, 1,0)), grid.getValue(ijk), | |
| 1836 | 526318 | grid.getValue(ijk.offsetBy(0,-1,0)) ); | |
| 1837 | } | ||
| 1838 | |||
| 1839 | template<typename Accessor> | ||
| 1840 | 526318 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 1841 | { | ||
| 1842 | 526318 | return difference( grid.getValue(ijk.offsetBy( 0,0, 1)), grid.getValue(ijk), | |
| 1843 | 526318 | grid.getValue(ijk.offsetBy( 0,0,-1)) ); | |
| 1844 | } | ||
| 1845 | |||
| 1846 | // cross derivatives | ||
| 1847 | template<typename Accessor> | ||
| 1848 | 526326 | static typename Accessor::ValueType inXandY(const Accessor& grid, const Coord& ijk) | |
| 1849 | { | ||
| 1850 | 526324 | return crossdifference( | |
| 1851 | 526326 | grid.getValue(ijk.offsetBy(1, 1,0)), grid.getValue(ijk.offsetBy( 1,-1,0)), | |
| 1852 | 526326 | grid.getValue(ijk.offsetBy(-1,1,0)), grid.getValue(ijk.offsetBy(-1,-1,0))); | |
| 1853 | |||
| 1854 | } | ||
| 1855 | |||
| 1856 | template<typename Accessor> | ||
| 1857 | 526326 | static typename Accessor::ValueType inXandZ(const Accessor& grid, const Coord& ijk) | |
| 1858 | { | ||
| 1859 | 526324 | return crossdifference( | |
| 1860 | 526326 | grid.getValue(ijk.offsetBy(1,0, 1)), grid.getValue(ijk.offsetBy(1, 0,-1)), | |
| 1861 | 526326 | grid.getValue(ijk.offsetBy(-1,0,1)), grid.getValue(ijk.offsetBy(-1,0,-1)) ); | |
| 1862 | } | ||
| 1863 | |||
| 1864 | template<typename Accessor> | ||
| 1865 | 263176 | static typename Accessor::ValueType inYandZ(const Accessor& grid, const Coord& ijk) | |
| 1866 | { | ||
| 1867 | 263174 | return crossdifference( | |
| 1868 | 263176 | grid.getValue(ijk.offsetBy(0, 1,1)), grid.getValue(ijk.offsetBy(0, 1,-1)), | |
| 1869 | 263176 | grid.getValue(ijk.offsetBy(0,-1,1)), grid.getValue(ijk.offsetBy(0,-1,-1)) ); | |
| 1870 | } | ||
| 1871 | |||
| 1872 | |||
| 1873 | // stencil access version | ||
| 1874 | template<typename Stencil> | ||
| 1875 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 1876 | { | ||
| 1877 | return difference( S.template getValue< 1, 0, 0>(), S.template getValue< 0, 0, 0>(), | ||
| 1878 | S.template getValue<-1, 0, 0>() ); | ||
| 1879 | } | ||
| 1880 | |||
| 1881 | template<typename Stencil> | ||
| 1882 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 1883 | { | ||
| 1884 | return difference( S.template getValue< 0, 1, 0>(), S.template getValue< 0, 0, 0>(), | ||
| 1885 | S.template getValue< 0,-1, 0>() ); | ||
| 1886 | } | ||
| 1887 | |||
| 1888 | template<typename Stencil> | ||
| 1889 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 1890 | { | ||
| 1891 | return difference( S.template getValue< 0, 0, 1>(), S.template getValue< 0, 0, 0>(), | ||
| 1892 | S.template getValue< 0, 0,-1>() ); | ||
| 1893 | } | ||
| 1894 | |||
| 1895 | // cross derivatives | ||
| 1896 | template<typename Stencil> | ||
| 1897 | static typename Stencil::ValueType inXandY(const Stencil& S) | ||
| 1898 | { | ||
| 1899 | return crossdifference(S.template getValue< 1, 1, 0>(), S.template getValue< 1,-1, 0>(), | ||
| 1900 | S.template getValue<-1, 1, 0>(), S.template getValue<-1,-1, 0>() ); | ||
| 1901 | } | ||
| 1902 | |||
| 1903 | template<typename Stencil> | ||
| 1904 | static typename Stencil::ValueType inXandZ(const Stencil& S) | ||
| 1905 | { | ||
| 1906 | return crossdifference(S.template getValue< 1, 0, 1>(), S.template getValue< 1, 0,-1>(), | ||
| 1907 | S.template getValue<-1, 0, 1>(), S.template getValue<-1, 0,-1>() ); | ||
| 1908 | } | ||
| 1909 | |||
| 1910 | template<typename Stencil> | ||
| 1911 | static typename Stencil::ValueType inYandZ(const Stencil& S) | ||
| 1912 | { | ||
| 1913 | return crossdifference(S.template getValue< 0, 1, 1>(), S.template getValue< 0, 1,-1>(), | ||
| 1914 | S.template getValue< 0,-1, 1>(), S.template getValue< 0,-1,-1>() ); | ||
| 1915 | } | ||
| 1916 | }; | ||
| 1917 | |||
| 1918 | |||
| 1919 | template<> | ||
| 1920 | struct D2<CD_FOURTH> | ||
| 1921 | { | ||
| 1922 | |||
| 1923 | // the difference opperator | ||
| 1924 | template <typename ValueType> | ||
| 1925 | static ValueType difference(const ValueType& xp2, const ValueType& xp1, const ValueType& xp0, | ||
| 1926 | const ValueType& xm1, const ValueType& xm2) { | ||
| 1927 | 9 | return ValueType(-1./12.)*(xp2 + xm2) + ValueType(4./3.)*(xp1 + xm1) -ValueType(2.5)*xp0; | |
| 1928 | } | ||
| 1929 | |||
| 1930 | template <typename ValueType> | ||
| 1931 | static ValueType crossdifference(const ValueType& xp2yp2, const ValueType& xp2yp1, | ||
| 1932 | const ValueType& xp2ym1, const ValueType& xp2ym2, | ||
| 1933 | const ValueType& xp1yp2, const ValueType& xp1yp1, | ||
| 1934 | const ValueType& xp1ym1, const ValueType& xp1ym2, | ||
| 1935 | const ValueType& xm2yp2, const ValueType& xm2yp1, | ||
| 1936 | const ValueType& xm2ym1, const ValueType& xm2ym2, | ||
| 1937 | const ValueType& xm1yp2, const ValueType& xm1yp1, | ||
| 1938 | const ValueType& xm1ym1, const ValueType& xm1ym2 ) { | ||
| 1939 | 27 | ValueType tmp1 = | |
| 1940 | 27 | ValueType(2./3.0)*(xp1yp1 - xm1yp1 - xp1ym1 + xm1ym1)- | |
| 1941 | 27 | ValueType(1./12.)*(xp2yp1 - xm2yp1 - xp2ym1 + xm2ym1); | |
| 1942 | 27 | ValueType tmp2 = | |
| 1943 | 27 | ValueType(2./3.0)*(xp1yp2 - xm1yp2 - xp1ym2 + xm1ym2)- | |
| 1944 | 27 | ValueType(1./12.)*(xp2yp2 - xm2yp2 - xp2ym2 + xm2ym2); | |
| 1945 | |||
| 1946 | 27 | return ValueType(2./3.)*tmp1 - ValueType(1./12.)*tmp2; | |
| 1947 | } | ||
| 1948 | |||
| 1949 | |||
| 1950 | |||
| 1951 | // random access version | ||
| 1952 | template<typename Accessor> | ||
| 1953 | 9 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 1954 | { | ||
| 1955 | 18 | return difference( | |
| 1956 | 9 | grid.getValue(ijk.offsetBy(2,0,0)), grid.getValue(ijk.offsetBy( 1,0,0)), | |
| 1957 | grid.getValue(ijk), | ||
| 1958 | 9 | grid.getValue(ijk.offsetBy(-1,0,0)), grid.getValue(ijk.offsetBy(-2, 0, 0))); | |
| 1959 | } | ||
| 1960 | |||
| 1961 | template<typename Accessor> | ||
| 1962 | 9 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 1963 | { | ||
| 1964 | 18 | return difference( | |
| 1965 | 9 | grid.getValue(ijk.offsetBy(0, 2,0)), grid.getValue(ijk.offsetBy(0, 1,0)), | |
| 1966 | grid.getValue(ijk), | ||
| 1967 | 9 | grid.getValue(ijk.offsetBy(0,-1,0)), grid.getValue(ijk.offsetBy(0,-2, 0))); | |
| 1968 | } | ||
| 1969 | |||
| 1970 | template<typename Accessor> | ||
| 1971 | 9 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 1972 | { | ||
| 1973 | 18 | return difference( | |
| 1974 | 9 | grid.getValue(ijk.offsetBy(0,0, 2)), grid.getValue(ijk.offsetBy(0, 0,1)), | |
| 1975 | grid.getValue(ijk), | ||
| 1976 | 9 | grid.getValue(ijk.offsetBy(0,0,-1)), grid.getValue(ijk.offsetBy(0,0,-2))); | |
| 1977 | } | ||
| 1978 | |||
| 1979 | // cross derivatives | ||
| 1980 | template<typename Accessor> | ||
| 1981 | 9 | static typename Accessor::ValueType inXandY(const Accessor& grid, const Coord& ijk) | |
| 1982 | { | ||
| 1983 | using ValueType = typename Accessor::ValueType; | ||
| 1984 | 9 | typename Accessor::ValueType tmp1 = | |
| 1985 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 1, 0)) - | |
| 1986 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0,-1, 0)); | |
| 1987 | 9 | typename Accessor::ValueType tmp2 = | |
| 1988 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 2, 0)) - | |
| 1989 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0,-2, 0)); | |
| 1990 | 9 | return ValueType(2./3.)*tmp1 - ValueType(1./12.)*tmp2; | |
| 1991 | } | ||
| 1992 | |||
| 1993 | template<typename Accessor> | ||
| 1994 | 9 | static typename Accessor::ValueType inXandZ(const Accessor& grid, const Coord& ijk) | |
| 1995 | { | ||
| 1996 | using ValueType = typename Accessor::ValueType; | ||
| 1997 | 9 | typename Accessor::ValueType tmp1 = | |
| 1998 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 0, 1)) - | |
| 1999 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 0,-1)); | |
| 2000 | 9 | typename Accessor::ValueType tmp2 = | |
| 2001 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 0, 2)) - | |
| 2002 | 9 | D1<CD_4TH>::inX(grid, ijk.offsetBy(0, 0,-2)); | |
| 2003 | 9 | return ValueType(2./3.)*tmp1 - ValueType(1./12.)*tmp2; | |
| 2004 | } | ||
| 2005 | |||
| 2006 | template<typename Accessor> | ||
| 2007 | 9 | static typename Accessor::ValueType inYandZ(const Accessor& grid, const Coord& ijk) | |
| 2008 | { | ||
| 2009 | using ValueType = typename Accessor::ValueType; | ||
| 2010 | 9 | typename Accessor::ValueType tmp1 = | |
| 2011 | 9 | D1<CD_4TH>::inY(grid, ijk.offsetBy(0, 0, 1)) - | |
| 2012 | 9 | D1<CD_4TH>::inY(grid, ijk.offsetBy(0, 0,-1)); | |
| 2013 | 9 | typename Accessor::ValueType tmp2 = | |
| 2014 | 9 | D1<CD_4TH>::inY(grid, ijk.offsetBy(0, 0, 2)) - | |
| 2015 | 9 | D1<CD_4TH>::inY(grid, ijk.offsetBy(0, 0,-2)); | |
| 2016 | 9 | return ValueType(2./3.)*tmp1 - ValueType(1./12.)*tmp2; | |
| 2017 | } | ||
| 2018 | |||
| 2019 | |||
| 2020 | // stencil access version | ||
| 2021 | template<typename Stencil> | ||
| 2022 | static typename Stencil::ValueType inX(const Stencil& S) | ||
| 2023 | { | ||
| 2024 | return difference(S.template getValue< 2, 0, 0>(), S.template getValue< 1, 0, 0>(), | ||
| 2025 | S.template getValue< 0, 0, 0>(), | ||
| 2026 | S.template getValue<-1, 0, 0>(), S.template getValue<-2, 0, 0>() ); | ||
| 2027 | } | ||
| 2028 | |||
| 2029 | template<typename Stencil> | ||
| 2030 | static typename Stencil::ValueType inY(const Stencil& S) | ||
| 2031 | { | ||
| 2032 | return difference(S.template getValue< 0, 2, 0>(), S.template getValue< 0, 1, 0>(), | ||
| 2033 | S.template getValue< 0, 0, 0>(), | ||
| 2034 | S.template getValue< 0,-1, 0>(), S.template getValue< 0,-2, 0>() ); | ||
| 2035 | } | ||
| 2036 | |||
| 2037 | template<typename Stencil> | ||
| 2038 | static typename Stencil::ValueType inZ(const Stencil& S) | ||
| 2039 | { | ||
| 2040 | return difference(S.template getValue< 0, 0, 2>(), S.template getValue< 0, 0, 1>(), | ||
| 2041 | S.template getValue< 0, 0, 0>(), | ||
| 2042 | S.template getValue< 0, 0,-1>(), S.template getValue< 0, 0,-2>() ); | ||
| 2043 | } | ||
| 2044 | |||
| 2045 | // cross derivatives | ||
| 2046 | template<typename Stencil> | ||
| 2047 | 9 | static typename Stencil::ValueType inXandY(const Stencil& S) | |
| 2048 | { | ||
| 2049 | return crossdifference( | ||
| 2050 | S.template getValue< 2, 2, 0>(), S.template getValue< 2, 1, 0>(), | ||
| 2051 | S.template getValue< 2,-1, 0>(), S.template getValue< 2,-2, 0>(), | ||
| 2052 | S.template getValue< 1, 2, 0>(), S.template getValue< 1, 1, 0>(), | ||
| 2053 | S.template getValue< 1,-1, 0>(), S.template getValue< 1,-2, 0>(), | ||
| 2054 | S.template getValue<-2, 2, 0>(), S.template getValue<-2, 1, 0>(), | ||
| 2055 | S.template getValue<-2,-1, 0>(), S.template getValue<-2,-2, 0>(), | ||
| 2056 | S.template getValue<-1, 2, 0>(), S.template getValue<-1, 1, 0>(), | ||
| 2057 | 9 | S.template getValue<-1,-1, 0>(), S.template getValue<-1,-2, 0>() ); | |
| 2058 | } | ||
| 2059 | |||
| 2060 | template<typename Stencil> | ||
| 2061 | 9 | static typename Stencil::ValueType inXandZ(const Stencil& S) | |
| 2062 | { | ||
| 2063 | return crossdifference( | ||
| 2064 | S.template getValue< 2, 0, 2>(), S.template getValue< 2, 0, 1>(), | ||
| 2065 | S.template getValue< 2, 0,-1>(), S.template getValue< 2, 0,-2>(), | ||
| 2066 | S.template getValue< 1, 0, 2>(), S.template getValue< 1, 0, 1>(), | ||
| 2067 | S.template getValue< 1, 0,-1>(), S.template getValue< 1, 0,-2>(), | ||
| 2068 | S.template getValue<-2, 0, 2>(), S.template getValue<-2, 0, 1>(), | ||
| 2069 | S.template getValue<-2, 0,-1>(), S.template getValue<-2, 0,-2>(), | ||
| 2070 | S.template getValue<-1, 0, 2>(), S.template getValue<-1, 0, 1>(), | ||
| 2071 | 9 | S.template getValue<-1, 0,-1>(), S.template getValue<-1, 0,-2>() ); | |
| 2072 | } | ||
| 2073 | |||
| 2074 | template<typename Stencil> | ||
| 2075 | 9 | static typename Stencil::ValueType inYandZ(const Stencil& S) | |
| 2076 | { | ||
| 2077 | return crossdifference( | ||
| 2078 | S.template getValue< 0, 2, 2>(), S.template getValue< 0, 2, 1>(), | ||
| 2079 | S.template getValue< 0, 2,-1>(), S.template getValue< 0, 2,-2>(), | ||
| 2080 | S.template getValue< 0, 1, 2>(), S.template getValue< 0, 1, 1>(), | ||
| 2081 | S.template getValue< 0, 1,-1>(), S.template getValue< 0, 1,-2>(), | ||
| 2082 | S.template getValue< 0,-2, 2>(), S.template getValue< 0,-2, 1>(), | ||
| 2083 | S.template getValue< 0,-2,-1>(), S.template getValue< 0,-2,-2>(), | ||
| 2084 | S.template getValue< 0,-1, 2>(), S.template getValue< 0,-1, 1>(), | ||
| 2085 | 9 | S.template getValue< 0,-1,-1>(), S.template getValue< 0,-1,-2>() ); | |
| 2086 | } | ||
| 2087 | }; | ||
| 2088 | |||
| 2089 | |||
| 2090 | template<> | ||
| 2091 | struct D2<CD_SIXTH> | ||
| 2092 | { | ||
| 2093 | // the difference opperator | ||
| 2094 | template <typename ValueType> | ||
| 2095 | static ValueType difference(const ValueType& xp3, const ValueType& xp2, const ValueType& xp1, | ||
| 2096 | const ValueType& xp0, | ||
| 2097 | const ValueType& xm1, const ValueType& xm2, const ValueType& xm3) | ||
| 2098 | { | ||
| 2099 | 48 | return ValueType(1./90.)*(xp3 + xm3) - ValueType(3./20.)*(xp2 + xm2) | |
| 2100 | 48 | + ValueType(1.5)*(xp1 + xm1) - ValueType(49./18.)*xp0; | |
| 2101 | } | ||
| 2102 | |||
| 2103 | template <typename ValueType> | ||
| 2104 | 24 | static ValueType crossdifference( const ValueType& xp1yp1,const ValueType& xm1yp1, | |
| 2105 | const ValueType& xp1ym1,const ValueType& xm1ym1, | ||
| 2106 | const ValueType& xp2yp1,const ValueType& xm2yp1, | ||
| 2107 | const ValueType& xp2ym1,const ValueType& xm2ym1, | ||
| 2108 | const ValueType& xp3yp1,const ValueType& xm3yp1, | ||
| 2109 | const ValueType& xp3ym1,const ValueType& xm3ym1, | ||
| 2110 | const ValueType& xp1yp2,const ValueType& xm1yp2, | ||
| 2111 | const ValueType& xp1ym2,const ValueType& xm1ym2, | ||
| 2112 | const ValueType& xp2yp2,const ValueType& xm2yp2, | ||
| 2113 | const ValueType& xp2ym2,const ValueType& xm2ym2, | ||
| 2114 | const ValueType& xp3yp2,const ValueType& xm3yp2, | ||
| 2115 | const ValueType& xp3ym2,const ValueType& xm3ym2, | ||
| 2116 | const ValueType& xp1yp3,const ValueType& xm1yp3, | ||
| 2117 | const ValueType& xp1ym3,const ValueType& xm1ym3, | ||
| 2118 | const ValueType& xp2yp3,const ValueType& xm2yp3, | ||
| 2119 | const ValueType& xp2ym3,const ValueType& xm2ym3, | ||
| 2120 | const ValueType& xp3yp3,const ValueType& xm3yp3, | ||
| 2121 | const ValueType& xp3ym3,const ValueType& xm3ym3 ) | ||
| 2122 | { | ||
| 2123 | 24 | ValueType tmp1 = | |
| 2124 | 24 | ValueType(0.7500)*(xp1yp1 - xm1yp1 - xp1ym1 + xm1ym1) - | |
| 2125 | 24 | ValueType(0.1500)*(xp2yp1 - xm2yp1 - xp2ym1 + xm2ym1) + | |
| 2126 | 24 | ValueType(1./60.)*(xp3yp1 - xm3yp1 - xp3ym1 + xm3ym1); | |
| 2127 | |||
| 2128 | 24 | ValueType tmp2 = | |
| 2129 | 24 | ValueType(0.7500)*(xp1yp2 - xm1yp2 - xp1ym2 + xm1ym2) - | |
| 2130 | 24 | ValueType(0.1500)*(xp2yp2 - xm2yp2 - xp2ym2 + xm2ym2) + | |
| 2131 | 24 | ValueType(1./60.)*(xp3yp2 - xm3yp2 - xp3ym2 + xm3ym2); | |
| 2132 | |||
| 2133 | 24 | ValueType tmp3 = | |
| 2134 | 24 | ValueType(0.7500)*(xp1yp3 - xm1yp3 - xp1ym3 + xm1ym3) - | |
| 2135 | 24 | ValueType(0.1500)*(xp2yp3 - xm2yp3 - xp2ym3 + xm2ym3) + | |
| 2136 | 24 | ValueType(1./60.)*(xp3yp3 - xm3yp3 - xp3ym3 + xm3ym3); | |
| 2137 | |||
| 2138 | 24 | return ValueType(0.75)*tmp1 - ValueType(0.15)*tmp2 + ValueType(1./60)*tmp3; | |
| 2139 | } | ||
| 2140 | |||
| 2141 | // random access version | ||
| 2142 | |||
| 2143 | template<typename Accessor> | ||
| 2144 | 8 | static typename Accessor::ValueType inX(const Accessor& grid, const Coord& ijk) | |
| 2145 | { | ||
| 2146 | 16 | return difference( | |
| 2147 | 8 | grid.getValue(ijk.offsetBy( 3, 0, 0)), grid.getValue(ijk.offsetBy( 2, 0, 0)), | |
| 2148 | 8 | grid.getValue(ijk.offsetBy( 1, 0, 0)), grid.getValue(ijk), | |
| 2149 | 8 | grid.getValue(ijk.offsetBy(-1, 0, 0)), grid.getValue(ijk.offsetBy(-2, 0, 0)), | |
| 2150 | 8 | grid.getValue(ijk.offsetBy(-3, 0, 0)) ); | |
| 2151 | } | ||
| 2152 | |||
| 2153 | template<typename Accessor> | ||
| 2154 | 8 | static typename Accessor::ValueType inY(const Accessor& grid, const Coord& ijk) | |
| 2155 | { | ||
| 2156 | 16 | return difference( | |
| 2157 | 8 | grid.getValue(ijk.offsetBy( 0, 3, 0)), grid.getValue(ijk.offsetBy( 0, 2, 0)), | |
| 2158 | 8 | grid.getValue(ijk.offsetBy( 0, 1, 0)), grid.getValue(ijk), | |
| 2159 | 8 | grid.getValue(ijk.offsetBy( 0,-1, 0)), grid.getValue(ijk.offsetBy( 0,-2, 0)), | |
| 2160 | 8 | grid.getValue(ijk.offsetBy( 0,-3, 0)) ); | |
| 2161 | } | ||
| 2162 | |||
| 2163 | template<typename Accessor> | ||
| 2164 | 8 | static typename Accessor::ValueType inZ(const Accessor& grid, const Coord& ijk) | |
| 2165 | { | ||
| 2166 | |||
| 2167 | 16 | return difference( | |
| 2168 | 8 | grid.getValue(ijk.offsetBy( 0, 0, 3)), grid.getValue(ijk.offsetBy( 0, 0, 2)), | |
| 2169 | 8 | grid.getValue(ijk.offsetBy( 0, 0, 1)), grid.getValue(ijk), | |
| 2170 | 8 | grid.getValue(ijk.offsetBy( 0, 0,-1)), grid.getValue(ijk.offsetBy( 0, 0,-2)), | |
| 2171 | 8 | grid.getValue(ijk.offsetBy( 0, 0,-3)) ); | |
| 2172 | } | ||
| 2173 | |||
| 2174 | template<typename Accessor> | ||
| 2175 | 8 | static typename Accessor::ValueType inXandY(const Accessor& grid, const Coord& ijk) | |
| 2176 | { | ||
| 2177 | using ValueT = typename Accessor::ValueType; | ||
| 2178 | 8 | ValueT tmp1 = | |
| 2179 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 1, 0)) - | |
| 2180 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0,-1, 0)); | |
| 2181 | 8 | ValueT tmp2 = | |
| 2182 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 2, 0)) - | |
| 2183 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0,-2, 0)); | |
| 2184 | 8 | ValueT tmp3 = | |
| 2185 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 3, 0)) - | |
| 2186 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0,-3, 0)); | |
| 2187 | 8 | return ValueT(0.75*tmp1 - 0.15*tmp2 + 1./60*tmp3); | |
| 2188 | } | ||
| 2189 | |||
| 2190 | template<typename Accessor> | ||
| 2191 | 8 | static typename Accessor::ValueType inXandZ(const Accessor& grid, const Coord& ijk) | |
| 2192 | { | ||
| 2193 | using ValueT = typename Accessor::ValueType; | ||
| 2194 | 8 | ValueT tmp1 = | |
| 2195 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0, 1)) - | |
| 2196 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0,-1)); | |
| 2197 | 8 | ValueT tmp2 = | |
| 2198 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0, 2)) - | |
| 2199 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0,-2)); | |
| 2200 | 8 | ValueT tmp3 = | |
| 2201 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0, 3)) - | |
| 2202 | 8 | D1<CD_6TH>::inX(grid, ijk.offsetBy(0, 0,-3)); | |
| 2203 | 8 | return ValueT(0.75*tmp1 - 0.15*tmp2 + 1./60*tmp3); | |
| 2204 | } | ||
| 2205 | |||
| 2206 | template<typename Accessor> | ||
| 2207 | 8 | static typename Accessor::ValueType inYandZ(const Accessor& grid, const Coord& ijk) | |
| 2208 | { | ||
| 2209 | using ValueT = typename Accessor::ValueType; | ||
| 2210 | 8 | ValueT tmp1 = | |
| 2211 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0, 1)) - | |
| 2212 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0,-1)); | |
| 2213 | 8 | ValueT tmp2 = | |
| 2214 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0, 2)) - | |
| 2215 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0,-2)); | |
| 2216 | 8 | ValueT tmp3 = | |
| 2217 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0, 3)) - | |
| 2218 | 8 | D1<CD_6TH>::inY(grid, ijk.offsetBy(0, 0,-3)); | |
| 2219 | 8 | return ValueT(0.75*tmp1 - 0.15*tmp2 + 1./60*tmp3); | |
| 2220 | } | ||
| 2221 | |||
| 2222 | |||
| 2223 | // stencil access version | ||
| 2224 | template<typename Stencil> | ||
| 2225 | 8 | static typename Stencil::ValueType inX(const Stencil& S) | |
| 2226 | { | ||
| 2227 | return difference( S.template getValue< 3, 0, 0>(), S.template getValue< 2, 0, 0>(), | ||
| 2228 | S.template getValue< 1, 0, 0>(), S.template getValue< 0, 0, 0>(), | ||
| 2229 | S.template getValue<-1, 0, 0>(), S.template getValue<-2, 0, 0>(), | ||
| 2230 | 8 | S.template getValue<-3, 0, 0>() ); | |
| 2231 | } | ||
| 2232 | |||
| 2233 | template<typename Stencil> | ||
| 2234 | 8 | static typename Stencil::ValueType inY(const Stencil& S) | |
| 2235 | { | ||
| 2236 | return difference( S.template getValue< 0, 3, 0>(), S.template getValue< 0, 2, 0>(), | ||
| 2237 | S.template getValue< 0, 1, 0>(), S.template getValue< 0, 0, 0>(), | ||
| 2238 | S.template getValue< 0,-1, 0>(), S.template getValue< 0,-2, 0>(), | ||
| 2239 | 8 | S.template getValue< 0,-3, 0>() ); | |
| 2240 | |||
| 2241 | } | ||
| 2242 | |||
| 2243 | template<typename Stencil> | ||
| 2244 | 8 | static typename Stencil::ValueType inZ(const Stencil& S) | |
| 2245 | { | ||
| 2246 | return difference( S.template getValue< 0, 0, 3>(), S.template getValue< 0, 0, 2>(), | ||
| 2247 | S.template getValue< 0, 0, 1>(), S.template getValue< 0, 0, 0>(), | ||
| 2248 | S.template getValue< 0, 0,-1>(), S.template getValue< 0, 0,-2>(), | ||
| 2249 | 8 | S.template getValue< 0, 0,-3>() ); | |
| 2250 | } | ||
| 2251 | |||
| 2252 | template<typename Stencil> | ||
| 2253 | 8 | static typename Stencil::ValueType inXandY(const Stencil& S) | |
| 2254 | { | ||
| 2255 | 8 | return crossdifference( S.template getValue< 1, 1, 0>(), S.template getValue<-1, 1, 0>(), | |
| 2256 | S.template getValue< 1,-1, 0>(), S.template getValue<-1,-1, 0>(), | ||
| 2257 | S.template getValue< 2, 1, 0>(), S.template getValue<-2, 1, 0>(), | ||
| 2258 | S.template getValue< 2,-1, 0>(), S.template getValue<-2,-1, 0>(), | ||
| 2259 | S.template getValue< 3, 1, 0>(), S.template getValue<-3, 1, 0>(), | ||
| 2260 | S.template getValue< 3,-1, 0>(), S.template getValue<-3,-1, 0>(), | ||
| 2261 | S.template getValue< 1, 2, 0>(), S.template getValue<-1, 2, 0>(), | ||
| 2262 | S.template getValue< 1,-2, 0>(), S.template getValue<-1,-2, 0>(), | ||
| 2263 | S.template getValue< 2, 2, 0>(), S.template getValue<-2, 2, 0>(), | ||
| 2264 | S.template getValue< 2,-2, 0>(), S.template getValue<-2,-2, 0>(), | ||
| 2265 | S.template getValue< 3, 2, 0>(), S.template getValue<-3, 2, 0>(), | ||
| 2266 | S.template getValue< 3,-2, 0>(), S.template getValue<-3,-2, 0>(), | ||
| 2267 | S.template getValue< 1, 3, 0>(), S.template getValue<-1, 3, 0>(), | ||
| 2268 | S.template getValue< 1,-3, 0>(), S.template getValue<-1,-3, 0>(), | ||
| 2269 | S.template getValue< 2, 3, 0>(), S.template getValue<-2, 3, 0>(), | ||
| 2270 | S.template getValue< 2,-3, 0>(), S.template getValue<-2,-3, 0>(), | ||
| 2271 | S.template getValue< 3, 3, 0>(), S.template getValue<-3, 3, 0>(), | ||
| 2272 | 8 | S.template getValue< 3,-3, 0>(), S.template getValue<-3,-3, 0>() ); | |
| 2273 | } | ||
| 2274 | |||
| 2275 | template<typename Stencil> | ||
| 2276 | 8 | static typename Stencil::ValueType inXandZ(const Stencil& S) | |
| 2277 | { | ||
| 2278 | 8 | return crossdifference( S.template getValue< 1, 0, 1>(), S.template getValue<-1, 0, 1>(), | |
| 2279 | S.template getValue< 1, 0,-1>(), S.template getValue<-1, 0,-1>(), | ||
| 2280 | S.template getValue< 2, 0, 1>(), S.template getValue<-2, 0, 1>(), | ||
| 2281 | S.template getValue< 2, 0,-1>(), S.template getValue<-2, 0,-1>(), | ||
| 2282 | S.template getValue< 3, 0, 1>(), S.template getValue<-3, 0, 1>(), | ||
| 2283 | S.template getValue< 3, 0,-1>(), S.template getValue<-3, 0,-1>(), | ||
| 2284 | S.template getValue< 1, 0, 2>(), S.template getValue<-1, 0, 2>(), | ||
| 2285 | S.template getValue< 1, 0,-2>(), S.template getValue<-1, 0,-2>(), | ||
| 2286 | S.template getValue< 2, 0, 2>(), S.template getValue<-2, 0, 2>(), | ||
| 2287 | S.template getValue< 2, 0,-2>(), S.template getValue<-2, 0,-2>(), | ||
| 2288 | S.template getValue< 3, 0, 2>(), S.template getValue<-3, 0, 2>(), | ||
| 2289 | S.template getValue< 3, 0,-2>(), S.template getValue<-3, 0,-2>(), | ||
| 2290 | S.template getValue< 1, 0, 3>(), S.template getValue<-1, 0, 3>(), | ||
| 2291 | S.template getValue< 1, 0,-3>(), S.template getValue<-1, 0,-3>(), | ||
| 2292 | S.template getValue< 2, 0, 3>(), S.template getValue<-2, 0, 3>(), | ||
| 2293 | S.template getValue< 2, 0,-3>(), S.template getValue<-2, 0,-3>(), | ||
| 2294 | S.template getValue< 3, 0, 3>(), S.template getValue<-3, 0, 3>(), | ||
| 2295 | 8 | S.template getValue< 3, 0,-3>(), S.template getValue<-3, 0,-3>() ); | |
| 2296 | } | ||
| 2297 | |||
| 2298 | template<typename Stencil> | ||
| 2299 | 8 | static typename Stencil::ValueType inYandZ(const Stencil& S) | |
| 2300 | { | ||
| 2301 | 8 | return crossdifference( S.template getValue< 0, 1, 1>(), S.template getValue< 0,-1, 1>(), | |
| 2302 | S.template getValue< 0, 1,-1>(), S.template getValue< 0,-1,-1>(), | ||
| 2303 | S.template getValue< 0, 2, 1>(), S.template getValue< 0,-2, 1>(), | ||
| 2304 | S.template getValue< 0, 2,-1>(), S.template getValue< 0,-2,-1>(), | ||
| 2305 | S.template getValue< 0, 3, 1>(), S.template getValue< 0,-3, 1>(), | ||
| 2306 | S.template getValue< 0, 3,-1>(), S.template getValue< 0,-3,-1>(), | ||
| 2307 | S.template getValue< 0, 1, 2>(), S.template getValue< 0,-1, 2>(), | ||
| 2308 | S.template getValue< 0, 1,-2>(), S.template getValue< 0,-1,-2>(), | ||
| 2309 | S.template getValue< 0, 2, 2>(), S.template getValue< 0,-2, 2>(), | ||
| 2310 | S.template getValue< 0, 2,-2>(), S.template getValue< 0,-2,-2>(), | ||
| 2311 | S.template getValue< 0, 3, 2>(), S.template getValue< 0,-3, 2>(), | ||
| 2312 | S.template getValue< 0, 3,-2>(), S.template getValue< 0,-3,-2>(), | ||
| 2313 | S.template getValue< 0, 1, 3>(), S.template getValue< 0,-1, 3>(), | ||
| 2314 | S.template getValue< 0, 1,-3>(), S.template getValue< 0,-1,-3>(), | ||
| 2315 | S.template getValue< 0, 2, 3>(), S.template getValue< 0,-2, 3>(), | ||
| 2316 | S.template getValue< 0, 2,-3>(), S.template getValue< 0,-2,-3>(), | ||
| 2317 | S.template getValue< 0, 3, 3>(), S.template getValue< 0,-3, 3>(), | ||
| 2318 | 8 | S.template getValue< 0, 3,-3>(), S.template getValue< 0,-3,-3>() ); | |
| 2319 | } | ||
| 2320 | |||
| 2321 | }; | ||
| 2322 | |||
| 2323 | } // end math namespace | ||
| 2324 | } // namespace OPENVDB_VERSION_NAME | ||
| 2325 | } // end openvdb namespace | ||
| 2326 | |||
| 2327 | #endif // OPENVDB_MATH_FINITEDIFFERENCE_HAS_BEEN_INCLUDED | ||
| 2328 |