Peter Gottschling committed Feb 15, 2008 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 // ============================================================================ // == == // == AMDiS - Adaptive multidimensional simulations == // == == // ============================================================================ // == == // == crystal growth group == // == == // == Stiftung caesar == // == Ludwig-Erhard-Allee 2 == // == 53175 Bonn == // == germany == // == == // ============================================================================ // == == // == http://www.caesar.de/cg/AMDiS == // == == // ============================================================================ /** \file Quadrature.h */ #ifndef AMDIS_QUADRATURE_H #define AMDIS_QUADRATURE_H #include "BasisFunction.h" #include "Flag.h" #include "MemoryManager.h" #include "FixVec.h" #include namespace AMDiS { template class WorldVector; template class DimVec; template class VectorOfFixVecs; template class MatrixOfFixVecs; // ============================================================================ // ===== class Quadrature ===================================================== // ============================================================================ /** * \ingroup Assembler * * \brief * For the assemblage of the system matrix and right hand side vector of the * linear system, we have to compute integrals, for example: * \f[ \int_{\Omega} f(x)\varphi_i(x) dx \f] * For general data A, b, c, and f, these integrals can not be calculated * exactly. Quadrature formulas have to be used in order to calculate the * integrals approximately. Numerical integration in finite element methods is * done by looping over all grid elements and using a quadrature formula on * each element. */ class Quadrature { public: MEMORY_MANAGED(Quadrature); protected: /** \brief * Avoids call of default constructor */ Quadrature(); /** \brief * Constructs a Quadrature with name name_ of degree degree_ for dim dim_. * The Quadrature has n_points_ quadrature points with barycentric * coordinates lambda_ and weights w_. The constructor is protected because * access to a Quadrature should be done via \ref provideQuadrature. */ Quadrature(const char* name_, int degree_, int dim_, int n_points_, VectorOfFixVecs > *lambda_, double* w_) : name(name_), degree(degree_), dim(dim_), n_points(n_points_), lambda(lambda_), w(w_) {}; /** \brief * Destructor */ ~Quadrature(); public: /** \brief * Copy constructor */ Quadrature(const Quadrature&); /** \brief * Returns a Quadrature for dimension dim_ exact for degree degree_. */ static Quadrature *provideQuadrature(int dim_, int degree_); /** \brief * Approximates an integral by the numerical quadrature described by quad; * f is a pointer to an AbstractFunction to be integrated, evaluated in * barycentric coordinates; the return value is * \f[ \sum_{k = 0}^{n_points-1} w[k] * (*f)(lambda[k]) \f] * For the approximation of \f$\int_S f\f$ we have to multiply this value * with d!|S| for a simplex S; for a parametric simplex f should be a pointer * to a function which calculates * \f$f(\lambda)|det DF_S(\hat{x}(\lambda))| \f$. */ double integrateStdSimplex(AbstractFunction > *f); /** \brief * Returns \ref name */  Thomas Witkowski committed May 07, 2008 117 118 119  inline const ::std::string& getName() { return name; };  Peter Gottschling committed Feb 15, 2008 120 121 122 123  /** \brief * Returns \ref n_points */  Thomas Witkowski committed May 07, 2008 124 125 126  inline int getNumPoints() const { return n_points; };  Peter Gottschling committed Feb 15, 2008 127 128 129 130  /** \brief * Returns \ref w[p] */  Thomas Witkowski committed May 07, 2008 131 132 133  inline double getWeight(int p) const { return w[p]; };  Peter Gottschling committed Feb 15, 2008 134 135 136 137  /** \brief * Returns \ref w. */  Thomas Witkowski committed May 07, 2008 138 139 140  inline double* getWeight() const { return w; };  Peter Gottschling committed Feb 15, 2008 141 142 143 144  /** \brief * Returns \ref dim */  Thomas Witkowski committed May 07, 2008 145 146 147  inline int getDim() const { return dim; };  Peter Gottschling committed Feb 15, 2008 148 149 150 151  /** \brief * Returns \ref degree */  Thomas Witkowski committed May 07, 2008 152 153 154  inline int getDegree() const { return degree; };  Peter Gottschling committed Feb 15, 2008 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184  /** \brief * Returns a pointer to a vector storing the values of a doubled valued * function at all quadrature points; f is that AbstractFunction * , evaluated in barycentric coordinates; if vec is not NULL, the values are * stored in this vector, otherwise the values are stored in some static * local vector, which is overwritten on the next call */ const double *fAtQp(const AbstractFunction >& f, double *vec) const ; /** \brief * Returns a pointer to a vector storing the gradient (with respect to world * coordinates) of a double valued function at all quadrature points; * grdF is a pointer to a AbstractFunction, evaluated in barycentric * coordinates and returning a pointer to a WorldVector storing the gradient; * if vec is not NULL, the values are stored in this vector, otherwise the * values are stored in some local static vector, which is overwritten on the * next call */ const WorldVector *grdFAtQp(const AbstractFunction, DimVec >& grdF, WorldVector* vec) const; /** \brief * Returns \ref lambda[a][b] which is the b-th coordinate entry of the a-th * quadrature point */  Thomas Witkowski committed May 07, 2008 185  inline double getLambda(int a, int b) const {  Peter Gottschling committed Feb 15, 2008 186 187 188 189 190 191 192 193 194 195 196 197 198 199  return (lambda ? (*lambda)[a][b] : 0.0); }; /** \brief * Returns \ref lambda[a] which is a DimVec containing the * coordiantes of the a-th quadrature point */ inline const DimVec& getLambda(int a) const { return (*lambda)[a]; }; /** \brief * Returns \ref lambda which is a VectorOfFixvecs >. */  Thomas Witkowski committed May 07, 2008 200 201 202  VectorOfFixVecs > *getLambda() const { return lambda; };  Peter Gottschling committed Feb 15, 2008 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632  public: /** \brief * Maximal number of quadrature points for the different dimensions */ static const int maxNQuadPoints[4]; protected: /** \brief * Name of this Quadrature */ ::std::string name; /** \brief * Quadrature is exact of this degree */ int degree; /** \brief * Quadrature for dimension dim */ int dim; /** \brief * Number of quadrature points */ int n_points; /** \brief * Vector of quadrature points given in barycentric coordinates */ VectorOfFixVecs > *lambda; /** \brief * Vector of quadrature weights */ double *w; protected: /** \brief * Initialisation of all static Quadrature objects which will be returned * by \ref provideQuadrature() */ static void initStaticQuadratures(); /** \name static quadratures, used weights, and barycentric coords * \{ */ static Quadrature **quad_nd[4]; static Quadrature *quad_0d[1]; static Quadrature *quad_1d[20]; static Quadrature *quad_2d[18]; static Quadrature *quad_3d[8]; static VectorOfFixVecs > *x_0d; static double *w_0d; static VectorOfFixVecs > *x0_1d; static VectorOfFixVecs > *x1_1d; static VectorOfFixVecs > *x2_1d; static VectorOfFixVecs > *x3_1d; static VectorOfFixVecs > *x4_1d; static VectorOfFixVecs > *x5_1d; static VectorOfFixVecs > *x6_1d; static VectorOfFixVecs > *x7_1d; static VectorOfFixVecs > *x8_1d; static VectorOfFixVecs > *x9_1d; static double *w0_1d; static double *w1_1d; static double *w2_1d; static double *w3_1d; static double *w4_1d; static double *w5_1d; static double *w6_1d; static double *w7_1d; static double *w8_1d; static double *w9_1d; static VectorOfFixVecs > *x1_2d; static VectorOfFixVecs > *x2_2d; static VectorOfFixVecs > *x3_2d; static VectorOfFixVecs > *x4_2d; static VectorOfFixVecs > *x5_2d; static VectorOfFixVecs > *x7_2d; static VectorOfFixVecs > *x8_2d; static VectorOfFixVecs > *x9_2d; static VectorOfFixVecs > *x10_2d; static VectorOfFixVecs > *x11_2d; static VectorOfFixVecs > *x12_2d; static VectorOfFixVecs > *x17_2d; static double *w1_2d; static double *w2_2d; static double *w3_2d; static double *w4_2d; static double *w5_2d; static double *w7_2d; static double *w8_2d; static double *w9_2d; static double *w10_2d; static double *w11_2d; static double *w12_2d; static double *w17_2d; static VectorOfFixVecs > *x1_3d; static VectorOfFixVecs > *x2_3d; static VectorOfFixVecs > *x3_3d; static VectorOfFixVecs > *x4_3d; static VectorOfFixVecs > *x5_3d; static VectorOfFixVecs > *x7_3d; static double *w1_3d; static double *w2_3d; static double *w3_3d; static double *w4_3d; static double *w5_3d; static double *w7_3d; /** \} */ }; // ============================================================================ // ===== class FastQuadrature ================================================= // ============================================================================ /** \brief * Pre-compute the values of all basis functions at all quadrature nodes; */ const Flag INIT_PHI=1; /** \brief * Pre-compute the gradients (with respect to the barycentric coordinates) of * all basis functions at all quadrature nodes */ const Flag INIT_GRD_PHI=2; /** \brief * pre-compute all 2nd derivatives (with respect to the barycentric * coordinates) of all basis functions at all quadrature nodes; */ const Flag INIT_D2_PHI=4; // ============================================================================ /** * \ingroup Integration * *\brief * Often numerical integration involves basis functions, such as the assembling * of the system matrix and right hand side, or the integration of finite * element functions. Since numerical quadrature involves only the values at * the quadrature points and the values of basis functions and its derivatives * are the same at these points for all elements of the grid, such routines can * be much more efficient, if they can use pre-computed values of the basis * functions at the quadrature points. In this case the basis functions do not * have to be evaluated for each quadrature point on every element newly. * Information that should be pre-computed can be specified by the following * symbolic constants: * \ref INIT_PHI, \ref INIT_GRD_PHI, \ref INIT_D2_PHI */ class FastQuadrature { public: MEMORY_MANAGED(FastQuadrature); protected: /** \brief * Constructs a FastQuadrature for the given Quadrature, BasisFunction, and * flag. */ FastQuadrature(BasisFunction* basFcts, Quadrature* quad, Flag flag) : init_flag(flag), phi(NULL), grdPhi(NULL), D2Phi(NULL), quadrature(quad), basisFunctions(basFcts) {}; /** \brief * Copy constructor */ FastQuadrature(const FastQuadrature&); /** \brief * Extended copy constructor */ FastQuadrature(const FastQuadrature&,const Flag); /** \brief * Destructor */ ~FastQuadrature(); public: /** \brief * Returns a FastQuadrature for the given BasisFunction, Quadrature, and * flags */ static FastQuadrature* provideFastQuadrature(const BasisFunction*, const Quadrature&, Flag); /** \brief * inits FastQuadrature like speciefied in flag */ void init(Flag init_flag); inline bool initialized(Flag flag) { if(flag == INIT_PHI) { return (phi != NULL); } if(flag == INIT_GRD_PHI) { return (grdPhi != NULL); } if(flag == INIT_D2_PHI) { return (D2Phi != NULL); } ERROR_EXIT("invalid flag\n"); return false; }; /** \brief * Returns \ref quadrature */ inline const Quadrature* getQuadrature() const { return quadrature; }; /** \brief * Returns \ref max_points */ inline int getMaxQuadPoints() { return max_points; }; /** \brief * Returns (*\ref D2Phi)[q][i][j][m] */ const double getSecDer(int q,int i ,int j, int m) const; /** \brief * Returns (*\ref D2Phi)[q] */ const VectorOfFixVecs > *getSecDer(int q) const; /** \brief * Returns (*\ref grdPhi)[q][i][j] */ const double getGradient(int q, int i ,int j) const; /** \brief * Returns (*\ref grdPhi)[q] */ VectorOfFixVecs >* getGradient(int q) const; /** \brief * Returns \ref phi[q][i] */ inline const double getPhi(int q,int i) const {return (phi)?phi[q][i]:0;}; /** \brief * Returns \ref phi[q] */ inline const double *getPhi(int q) const {return (phi)?phi[q]:0;}; /** \brief * Returns \ref quadrature ->integrateStdSimplex(f) */ inline double integrateStdSimplex(AbstractFunction > *f) { return quadrature->integrateStdSimplex(f); }; /** \brief * Returns \ref quadrature ->getNumPoints() */ inline int getNumPoints() const { return quadrature->getNumPoints();}; /** \brief * Returns \ref quadrature ->getWeight(p) */ inline double getWeight(int p) const {return quadrature->getWeight(p);}; /** \brief * Returns \ref quadrature ->getDim() */ inline int getDim() const { return quadrature->getDim(); }; /** \brief * Returns \ref quadrature ->getDegree() */ inline int getDegree() const { return quadrature->getDegree(); }; /** \brief * Returns \ref quadrature ->grdFAtQp(f, vec) */ inline const WorldVector *grdFAtQp(const AbstractFunction, DimVec >& f, WorldVector* vec) const { return quadrature->grdFAtQp(f, vec); }; /** \brief * Returns \ref quadrature ->fAtQp(f, vec) */ inline const double *fAtQp(const AbstractFunction >& f,double *vec) const { return quadrature->fAtQp(f, vec); }; /** \brief * Returns \ref quadrature ->getLambda(a,b) */ inline double getLambda(int a,int b) const { return quadrature->getLambda(a,b); }; /** \brief * Returns \ref quadrature ->getLambda(a) */ inline const DimVec& getLambda(int a) const { return quadrature->getLambda(a); }; /** \brief * Returns \ref basisFunctions */ inline BasisFunction* getBasisFunctions() const { return basisFunctions; }; /** \brief * The function returns a pointer ptr to a vector of length * \ref quadrature->n_points storing the values of \f$u_h \f$ at all * quadrature points of \ref quadrature, i.e. * \f[ ptr[l] = u_h(quadrature->lambda[l]) \f] where * l = 0, . . . , quadrature->n_points - 1; the \ref INIT_PHI flag must * be set in \ref init_flag; vec is an optional memory pointer */ // const double *uhAtQp(const double *uh_loc, double *vec) const; /** \brief * The function returns a pointer ptr to a vector of length * quadrature->n_points WorldVectors storing \f$\nabla u_h \f$ at all * quadrature points of \ref quadrature, i.e. * \f[ ptr[l][i] = u_{h,xi}(quadrature->lambda[l]) \f] * where l = 0, ... , quadrature->n_points - 1, and i = 0, ... , * DIM_OF_WORLD - 1; the \ref INIT_GRD_PHI flag must be set in * \ref init flag; vec is an optional memory pointer */ // const WorldVector *grdUhAtQp(const DimVec >& Lambda, // const double *uh_loc, // WorldVector *vec) const; /** \brief * The function returns a pointer ptr to a vector of length * quadrarure->n_points of WorldMatrices storing D2uh at all quadrature * points of \ref quadrature, i.e. * \f[ ptr[l][i][j] = u_{h,x_ix_j}(quadrature->lambda[l]) \f] * where l = 0, ... , quadrature->n_points - 1, and i, j = 0, ... , * DIM_OF_WORLD - 1; the \ref INIT_D2_PHI flag must be set in * \ref init flag; vec is an optional memory pointer */ // const WorldMatrix *D2UhAtQp(const DimVec >& Lambda, // const double *uh_loc, // WorldMatrix *vec) const; protected: /** \brief * Specifies which information should be pre-computed. Can be \ref INIT_PHI, * \ref INIT_GRD_PHI, or \ref INIT_D2_PHI */ Flag init_flag; /** \brief * Matrix storing function values if the flag \ref INIT_PHI is set; * phi[i][j] stores the value \ref basisFunctions->phi[j] * (quadrature->lambda[i]), 0 <= j < basisFunctions->getNumber() and * 0 <= i < n_points */ double **phi; /** \brief * Matrix storing all gradients (with respect to the barycentric coordinates) * if the flag \ref INIT_GRD_PHI is set; grdPhi[i][j][k] stores the value * basisFunctions->grdPhi[j](quadrature->lambda[i])[k] * for 0 <= j < basisFunctions->getNumber(), * 0 <= i < . . . , n_points, and 0 <= k < DIM */ MatrixOfFixVecs > *grdPhi; /** \brief * Matrix storing all second derivatives (with respect to the barycentric * coordinates) if the flag \ref INIT_D2_PHI is set; D2Phi[i][j][k][l] stores * the value basisFunctions->D2Phi[j](quadrature->lambda[i])[k][l] * for 0 <= j < basisFunctions->getNumber(), * 0 <= i < n_points, and 0 <= k,l < DIM */ MatrixOfFixVecs > *D2Phi; /** \brief * List of all used FastQuadratures */ static ::std::list fastQuadList; /** \brief * Maximal number of quadrature points for all yet initialised FastQuadrature * objects. This value may change after a new initialisation of a * FastQuadrature */ static int max_points; /** \brief * This FastQuadrature stores values for Quadrature quadrature */ Quadrature* quadrature; /** \brief * Values stored for basis functions basisFunctions */ BasisFunction* basisFunctions; }; } #endif // AMDIS_QUADRATURE_H