1 /* 2 Common tools for constructing discretizations 3 */ 4 #if !defined(PETSCDT_H) 5 #define PETSCDT_H 6 7 #include <petscsys.h> 8 9 PETSC_EXTERN PetscClassId PETSCQUADRATURE_CLASSID; 10 11 /*S 12 PetscQuadrature - Quadrature rule for integration. 13 14 Level: beginner 15 16 .seealso: PetscQuadratureCreate(), PetscQuadratureDestroy() 17 S*/ 18 typedef struct _p_PetscQuadrature *PetscQuadrature; 19 20 /*E 21 PetscGaussLobattoLegendreCreateType - algorithm used to compute the Gauss-Lobatto-Legendre nodes and weights 22 23 Level: intermediate 24 25 $ PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA - compute the nodes via linear algebra 26 $ PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON - compute the nodes by solving a nonlinear equation with Newton's method 27 28 E*/ 29 typedef enum {PETSCGAUSSLOBATTOLEGENDRE_VIA_LINEAR_ALGEBRA,PETSCGAUSSLOBATTOLEGENDRE_VIA_NEWTON} PetscGaussLobattoLegendreCreateType; 30 31 PETSC_EXTERN PetscErrorCode PetscQuadratureCreate(MPI_Comm, PetscQuadrature *); 32 PETSC_EXTERN PetscErrorCode PetscQuadratureDuplicate(PetscQuadrature, PetscQuadrature *); 33 PETSC_EXTERN PetscErrorCode PetscQuadratureGetOrder(PetscQuadrature, PetscInt*); 34 PETSC_EXTERN PetscErrorCode PetscQuadratureSetOrder(PetscQuadrature, PetscInt); 35 PETSC_EXTERN PetscErrorCode PetscQuadratureGetNumComponents(PetscQuadrature, PetscInt*); 36 PETSC_EXTERN PetscErrorCode PetscQuadratureSetNumComponents(PetscQuadrature, PetscInt); 37 PETSC_EXTERN PetscErrorCode PetscQuadratureGetData(PetscQuadrature, PetscInt*, PetscInt*, PetscInt*, const PetscReal *[], const PetscReal *[]); 38 PETSC_EXTERN PetscErrorCode PetscQuadratureSetData(PetscQuadrature, PetscInt, PetscInt, PetscInt, const PetscReal [], const PetscReal []); 39 PETSC_EXTERN PetscErrorCode PetscQuadratureView(PetscQuadrature, PetscViewer); 40 PETSC_EXTERN PetscErrorCode PetscQuadratureDestroy(PetscQuadrature *); 41 42 PETSC_EXTERN PetscErrorCode PetscQuadratureExpandComposite(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], PetscQuadrature *); 43 44 PETSC_EXTERN PetscErrorCode PetscQuadraturePushForward(PetscQuadrature, PetscInt, const PetscReal[], const PetscReal[], const PetscReal[], PetscInt, PetscQuadrature *); 45 46 PETSC_EXTERN PetscErrorCode PetscDTLegendreEval(PetscInt,const PetscReal*,PetscInt,const PetscInt*,PetscReal*,PetscReal*,PetscReal*); 47 PETSC_EXTERN PetscErrorCode PetscDTGaussQuadrature(PetscInt,PetscReal,PetscReal,PetscReal*,PetscReal*); 48 PETSC_EXTERN PetscErrorCode PetscDTGaussLobattoLegendreQuadrature(PetscInt,PetscGaussLobattoLegendreCreateType,PetscReal*,PetscReal*); 49 PETSC_EXTERN PetscErrorCode PetscDTReconstructPoly(PetscInt,PetscInt,const PetscReal*,PetscInt,const PetscReal*,PetscReal*); 50 PETSC_EXTERN PetscErrorCode PetscDTGaussTensorQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*); 51 PETSC_EXTERN PetscErrorCode PetscDTGaussJacobiQuadrature(PetscInt,PetscInt,PetscInt,PetscReal,PetscReal,PetscQuadrature*); 52 53 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhTensorQuadrature(PetscInt, PetscInt, PetscReal, PetscReal, PetscQuadrature *); 54 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrate(void (*)(PetscReal, PetscReal *), PetscReal, PetscReal, PetscInt, PetscReal *); 55 PETSC_EXTERN PetscErrorCode PetscDTTanhSinhIntegrateMPFR(void (*)(PetscReal, PetscReal *), PetscReal, PetscReal, PetscInt, PetscReal *); 56 57 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreIntegrate(PetscInt, PetscReal *, PetscReal *, const PetscReal *, PetscReal *); 58 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 59 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementLaplacianDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 60 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 61 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementGradientDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***, PetscReal ***); 62 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 63 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementAdvectionDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 64 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassCreate(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 65 PETSC_EXTERN PetscErrorCode PetscGaussLobattoLegendreElementMassDestroy(PetscInt, PetscReal *, PetscReal *, PetscReal ***); 66 67 PETSC_EXTERN PetscErrorCode PetscDTAltVApply(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 68 PETSC_EXTERN PetscErrorCode PetscDTAltVWedge(PetscInt, PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 69 PETSC_EXTERN PetscErrorCode PetscDTAltVWedgeMatrix(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 70 PETSC_EXTERN PetscErrorCode PetscDTAltVPullback(PetscInt, PetscInt, const PetscReal *, PetscInt, const PetscReal *, PetscReal *); 71 PETSC_EXTERN PetscErrorCode PetscDTAltVPullbackMatrix(PetscInt, PetscInt, const PetscReal *, PetscInt, PetscReal *); 72 PETSC_EXTERN PetscErrorCode PetscDTAltVInterior(PetscInt, PetscInt, const PetscReal *, const PetscReal *, PetscReal *); 73 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorMatrix(PetscInt, PetscInt, const PetscReal *, PetscReal *); 74 PETSC_EXTERN PetscErrorCode PetscDTAltVInteriorPattern(PetscInt, PetscInt, PetscInt (*)[3]); 75 PETSC_EXTERN PetscErrorCode PetscDTAltVStar(PetscInt, PetscInt, PetscInt, const PetscReal *, PetscReal *); 76 77 #if defined(PETSC_USE_64BIT_INDICES) 78 #define PETSC_FACTORIAL_MAX 20 79 #define PETSC_BINOMIAL_MAX 61 80 #else 81 #define PETSC_FACTORIAL_MAX 12 82 #define PETSC_BINOMIAL_MAX 29 83 #endif 84 85 /*MC 86 PetscDTFactorial - Approximate n! as a real number 87 88 Input Arguments: 89 . n - a non-negative integer 90 91 Output Arguments: 92 . factorial - n! 93 94 Level: beginner 95 M*/ 96 PETSC_STATIC_INLINE PetscErrorCode PetscDTFactorial(PetscInt n, PetscReal *factorial) 97 { 98 PetscReal f = 1.0; 99 PetscInt i; 100 101 PetscFunctionBegin; 102 *factorial = -1.0; 103 if (n < 0) SETERRQ1(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Factorial called with negative number %D\n", n); 104 for (i = 1; i < n+1; ++i) f *= (PetscReal)i; 105 *factorial = f; 106 PetscFunctionReturn(0); 107 } 108 109 /*MC 110 PetscDTFactorialInt - Compute n! as an integer 111 112 Input Arguments: 113 . n - a non-negative integer 114 115 Output Arguments: 116 . factorial - n! 117 118 Level: beginner 119 120 Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer. 121 M*/ 122 PETSC_STATIC_INLINE PetscErrorCode PetscDTFactorialInt(PetscInt n, PetscInt *factorial) 123 { 124 PetscInt facLookup[13] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600}; 125 126 PetscFunctionBegin; 127 *factorial = -1; 128 if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX); 129 if (n <= 12) { 130 *factorial = facLookup[n]; 131 } else { 132 PetscInt f = facLookup[12]; 133 PetscInt i; 134 135 for (i = 13; i < n+1; ++i) f *= i; 136 *factorial = f; 137 } 138 PetscFunctionReturn(0); 139 } 140 141 /*MC 142 PetscDTBinomial - Approximate the binomial coefficient "n choose k" 143 144 Input Arguments: 145 + n - a non-negative integer 146 - k - an integer between 0 and n, inclusive 147 148 Output Arguments: 149 . binomial - approximation of the binomial coefficient n choose k 150 151 Level: beginner 152 M*/ 153 PETSC_STATIC_INLINE PetscErrorCode PetscDTBinomial(PetscInt n, PetscInt k, PetscReal *binomial) 154 { 155 PetscFunctionBeginHot; 156 *binomial = -1.0; 157 if (n < 0 || k < 0 || k > n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%D %D) must be non-negative, k <= n\n", n, k); 158 if (n <= 3) { 159 PetscInt binomLookup[4][4] = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}}; 160 161 *binomial = (PetscReal)binomLookup[n][k]; 162 } else { 163 PetscReal binom = 1.0; 164 PetscInt i; 165 166 k = PetscMin(k, n - k); 167 for (i = 0; i < k; i++) binom = (binom * (PetscReal)(n - i)) / (PetscReal)(i + 1); 168 *binomial = binom; 169 } 170 PetscFunctionReturn(0); 171 } 172 173 /*MC 174 PetscDTBinomialInt - Compute the binomial coefficient "n choose k" 175 176 Input Arguments: 177 + n - a non-negative integer 178 - k - an integer between 0 and n, inclusive 179 180 Output Arguments: 181 . binomial - the binomial coefficient n choose k 182 183 Note: this is limited by integers that can be represented by PetscInt 184 185 Level: beginner 186 M*/ 187 PETSC_STATIC_INLINE PetscErrorCode PetscDTBinomialInt(PetscInt n, PetscInt k, PetscInt *binomial) 188 { 189 PetscInt bin; 190 191 PetscFunctionBegin; 192 *binomial = -1; 193 if (n < 0 || k < 0 || k > n) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial arguments (%D %D) must be non-negative, k <= n\n", n, k); 194 if (n > PETSC_BINOMIAL_MAX) SETERRQ2(PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "Binomial elements %D is larger than max for PetscInt, %D\n", n, PETSC_BINOMIAL_MAX); 195 if (n <= 3) { 196 PetscInt binomLookup[4][4] = {{1, 0, 0, 0}, {1, 1, 0, 0}, {1, 2, 1, 0}, {1, 3, 3, 1}}; 197 198 bin = binomLookup[n][k]; 199 } else { 200 PetscInt binom = 1; 201 PetscInt i; 202 203 k = PetscMin(k, n - k); 204 for (i = 0; i < k; i++) binom = (binom * (n - i)) / (i + 1); 205 bin = binom; 206 } 207 *binomial = bin; 208 PetscFunctionReturn(0); 209 } 210 211 /*MC 212 PetscDTEnumPerm - Get a permutation of n integers from its encoding into the integers [0, n!) as a sequence of swaps. 213 214 A permutation can be described by the operations that convert the lists [0, 1, ..., n-1] into the permutation, 215 by a sequence of swaps, where the ith step swaps whatever number is in ith position with a number that is in 216 some position j >= i. This swap is encoded as the difference (j - i). The difference d_i at step i is less than 217 (n - i). This sequence of n-1 differences [d_0, ..., d_{n-2}] is encoded as the number 218 (n-1)! * d_0 + (n-2)! * d_1 + ... + 1! * d_{n-2}. 219 220 Input Arguments: 221 + n - a non-negative integer (see note about limits below) 222 - k - an integer in [0, n!) 223 224 Output Arguments: 225 + perm - the permuted list of the integers [0, ..., n-1] 226 - isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps. 227 228 Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer. 229 230 Level: beginner 231 M*/ 232 PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumPerm(PetscInt n, PetscInt k, PetscInt *perm, PetscBool *isOdd) 233 { 234 PetscInt odd = 0; 235 PetscInt i; 236 PetscInt work[PETSC_FACTORIAL_MAX]; 237 PetscInt *w; 238 239 PetscFunctionBegin; 240 if (isOdd) *isOdd = PETSC_FALSE; 241 if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX); 242 w = &work[n - 2]; 243 for (i = 2; i <= n; i++) { 244 *(w--) = k % i; 245 k /= i; 246 } 247 for (i = 0; i < n; i++) perm[i] = i; 248 for (i = 0; i < n - 1; i++) { 249 PetscInt s = work[i]; 250 PetscInt swap = perm[i]; 251 252 perm[i] = perm[i + s]; 253 perm[i + s] = swap; 254 odd ^= (!!s); 255 } 256 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 257 PetscFunctionReturn(0); 258 } 259 260 /*MC 261 PetscDTPermIndex - Encode a permutation of n into an integer in [0, n!). This inverts PetscDTEnumPerm. 262 263 Input Arguments: 264 + n - a non-negative integer (see note about limits below) 265 - perm - the permuted list of the integers [0, ..., n-1] 266 267 Output Arguments: 268 + k - an integer in [0, n!) 269 . isOdd - if not NULL, returns wether the permutation used an even or odd number of swaps. 270 271 Note: this is limited to n such that n! can be represented by PetscInt, which is 12 if PetscInt is a signed 32-bit integer and 20 if PetscInt is a signed 64-bit integer. 272 273 Level: beginner 274 M*/ 275 PETSC_STATIC_INLINE PetscErrorCode PetscDTPermIndex(PetscInt n, const PetscInt *perm, PetscInt *k, PetscBool *isOdd) 276 { 277 PetscInt odd = 0; 278 PetscInt i, idx; 279 PetscInt work[PETSC_FACTORIAL_MAX]; 280 PetscInt iwork[PETSC_FACTORIAL_MAX]; 281 282 PetscFunctionBeginHot; 283 *k = -1; 284 if (isOdd) *isOdd = PETSC_FALSE; 285 if (n < 0 || n > PETSC_FACTORIAL_MAX) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Number of elements %D is not in supported range [0,%D]\n",n,PETSC_FACTORIAL_MAX); 286 for (i = 0; i < n; i++) work[i] = i; /* partial permutation */ 287 for (i = 0; i < n; i++) iwork[i] = i; /* partial permutation inverse */ 288 for (idx = 0, i = 0; i < n - 1; i++) { 289 PetscInt j = perm[i]; 290 PetscInt icur = work[i]; 291 PetscInt jloc = iwork[j]; 292 PetscInt diff = jloc - i; 293 294 idx = idx * (n - i) + diff; 295 /* swap (i, jloc) */ 296 work[i] = j; 297 work[jloc] = icur; 298 iwork[j] = i; 299 iwork[icur] = jloc; 300 odd ^= (!!diff); 301 } 302 *k = idx; 303 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 304 PetscFunctionReturn(0); 305 } 306 307 /*MC 308 PetscDTEnumSubset - Get an ordered subset of the integers [0, ..., n - 1] from its encoding as an integers in [0, n choose k). 309 The encoding is in lexicographic order. 310 311 Input Arguments: 312 + n - a non-negative integer (see note about limits below) 313 . k - an integer in [0, n] 314 - j - an index in [0, n choose k) 315 316 Output Arguments: 317 . subset - the jth subset of size k of the integers [0, ..., n - 1] 318 319 Note: this is limited by arguments such that n choose k can be represented by PetscInt 320 321 Level: beginner 322 323 .seealso: PetscDTSubsetIndex() 324 M*/ 325 PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumSubset(PetscInt n, PetscInt k, PetscInt j, PetscInt *subset) 326 { 327 PetscInt Nk, i, l; 328 PetscErrorCode ierr; 329 330 PetscFunctionBeginHot; 331 ierr = PetscDTBinomialInt(n, k, &Nk);CHKERRQ(ierr); 332 for (i = 0, l = 0; i < n && l < k; i++) { 333 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 334 PetscInt Nminusk = Nk - Nminuskminus; 335 336 if (j < Nminuskminus) { 337 subset[l++] = i; 338 Nk = Nminuskminus; 339 } else { 340 j -= Nminuskminus; 341 Nk = Nminusk; 342 } 343 } 344 PetscFunctionReturn(0); 345 } 346 347 /*MC 348 PetscDTSubsetIndex - Convert an ordered subset of k integers from the set [0, ..., n - 1] to its encoding as an integers in [0, n choose k) in lexicographic order. This is the inverse of PetscDTEnumSubset. 349 350 Input Arguments: 351 + n - a non-negative integer (see note about limits below) 352 . k - an integer in [0, n] 353 - subset - an ordered subset of the integers [0, ..., n - 1] 354 355 Output Arguments: 356 . index - the rank of the subset in lexicographic order 357 358 Note: this is limited by arguments such that n choose k can be represented by PetscInt 359 360 Level: beginner 361 362 .seealso: PetscDTEnumSubset() 363 M*/ 364 PETSC_STATIC_INLINE PetscErrorCode PetscDTSubsetIndex(PetscInt n, PetscInt k, const PetscInt *subset, PetscInt *index) 365 { 366 PetscInt i, j = 0, l, Nk; 367 PetscErrorCode ierr; 368 369 PetscFunctionBegin; 370 *index = -1; 371 ierr = PetscDTBinomialInt(n, k, &Nk);CHKERRQ(ierr); 372 for (i = 0, l = 0; i < n && l < k; i++) { 373 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 374 PetscInt Nminusk = Nk - Nminuskminus; 375 376 if (subset[l] == i) { 377 l++; 378 Nk = Nminuskminus; 379 } else { 380 j += Nminuskminus; 381 Nk = Nminusk; 382 } 383 } 384 *index = j; 385 PetscFunctionReturn(0); 386 } 387 388 /*MC 389 PetscDTEnumSubset - Split the integers [0, ..., n - 1] into two complementary ordered subsets, the first subset of size k and being the jth subset of that size in lexicographic order. 390 391 Input Arguments: 392 + n - a non-negative integer (see note about limits below) 393 . k - an integer in [0, n] 394 - j - an index in [0, n choose k) 395 396 Output Arguments: 397 + perm - the jth subset of size k of the integers [0, ..., n - 1], followed by its complementary set. 398 - isOdd - if not NULL, return whether perm is an even or odd permutation. 399 400 Note: this is limited by arguments such that n choose k can be represented by PetscInt 401 402 Level: beginner 403 404 .seealso: PetscDTEnumSubset(), PetscDTSubsetIndex() 405 M*/ 406 PETSC_STATIC_INLINE PetscErrorCode PetscDTEnumSplit(PetscInt n, PetscInt k, PetscInt j, PetscInt *perm, PetscBool *isOdd) 407 { 408 PetscInt i, l, m, *subcomp, Nk; 409 PetscInt odd; 410 PetscErrorCode ierr; 411 412 PetscFunctionBegin; 413 if (isOdd) *isOdd = PETSC_FALSE; 414 ierr = PetscDTBinomialInt(n, k, &Nk);CHKERRQ(ierr); 415 odd = 0; 416 subcomp = &perm[k]; 417 for (i = 0, l = 0, m = 0; i < n && l < k; i++) { 418 PetscInt Nminuskminus = (Nk * (k - l)) / (n - i); 419 PetscInt Nminusk = Nk - Nminuskminus; 420 421 if (j < Nminuskminus) { 422 perm[l++] = i; 423 Nk = Nminuskminus; 424 } else { 425 subcomp[m++] = i; 426 j -= Nminuskminus; 427 odd ^= ((k - l) & 1); 428 Nk = Nminusk; 429 } 430 } 431 for (; i < n; i++) { 432 subcomp[m++] = i; 433 } 434 if (isOdd) *isOdd = odd ? PETSC_TRUE : PETSC_FALSE; 435 PetscFunctionReturn(0); 436 } 437 438 struct _p_PetscTabulation { 439 PetscInt K; /* Indicates a k-jet, namely tabulated derviatives up to order k */ 440 PetscInt Nr; /* THe number of tabulation replicas (often 1) */ 441 PetscInt Np; /* The number of tabulation points in a replica */ 442 PetscInt Nb; /* The number of functions tabulated */ 443 PetscInt Nc; /* The number of function components */ 444 PetscInt cdim; /* The coordinate dimension */ 445 PetscReal **T; /* The tabulation T[K] of functions and their derivatives 446 T[0] = B[Nr*Np][Nb][Nc]: The basis function values at quadrature points 447 T[1] = D[Nr*Np][Nb][Nc][cdim]: The basis function derivatives at quadrature points 448 T[2] = H[Nr*Np][Nb][Nc][cdim][cdim]: The basis function second derivatives at quadrature points */ 449 }; 450 typedef struct _p_PetscTabulation *PetscTabulation; 451 452 #endif 453