BasisFunction.h 14.6 KB
 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 // ============================================================================ // == == // == AMDiS - Adaptive multidimensional simulations == // == == // ============================================================================ // == == // == crystal growth group == // == == // == Stiftung caesar == // == Ludwig-Erhard-Allee 2 == // == 53175 Bonn == // == germany == // == == // ============================================================================ // == == // == http://www.caesar.de/cg/AMDiS == // == == // ============================================================================ /** \file BasisFunction.h */ #ifndef AMDIS_BASISFUNCTION_H #define AMDIS_BASISFUNCTION_H // ============================================================================ // ===== includes ============================================================= // ============================================================================ #include #include "Global.h" #include "Boundary.h" namespace AMDiS { // ============================================================================ // ===== forward declarations ================================================= // ============================================================================ class DOFAdmin; //template class DOFMatrix; class Element; class ElInfo; class RCNeighbourList; template class WorldVector; template class WorldMatrix; class Quadrature; template class AbstractFunction; template class DOFVector; template class DOFIndexed; template class DimVec; template class DimMat; template class FixVec; template class VectorOfFixVecs; // ============================================================================ // ===== typedefs ============================================================= // ============================================================================ typedef AbstractFunction > BasFctType; typedef AbstractFunction, DimVec > GrdBasFctType; typedef AbstractFunction, DimVec > D2BasFctType; typedef BasFctType *BFptr; typedef GrdBasFctType *GBFptr; typedef D2BasFctType *DBFptr; // ============================================================================ // ===== class BasisFunction ================================================== // ============================================================================ /** \ingroup FEMSpace * \brief * Base class for finite element basis functions. In order to build up a * finite element space, we have to specify a set of local basis functions. * Together with the correspondig DOF administration and the underlying mesh, * the finite element space is given. * This class holds the local basis functions and their derivatives of the * reference element. They are evaluated at barycentric coordinates, so they * can be used on every element of the mesh. */ class BasisFunction { protected: /** \brief * Creates a BasisFunction object of given dim and degree */ BasisFunction(const ::std::string& name_, int dim_, int degree_); /** \brief * destructor */ virtual ~BasisFunction(); public: /** \brief * compares two BasisFunction objects. */ virtual bool operator==(const BasisFunction& a) const {  Thomas Witkowski committed Apr 15, 2008 99  return a.getName() == name;  Peter Gottschling committed Feb 15, 2008 100 101 102 103 104 105  }; /** \brief * Returns !(*this == b) */ inline bool operator!=(const BasisFunction& b) const {  Thomas Witkowski committed Apr 15, 2008 106  return !(operator == (b));  Peter Gottschling committed Feb 15, 2008 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327  }; /** \brief * Used by \ref getDOFIndices and \ref getVec */ virtual int* orderOfPositionIndices(const Element* el, GeoIndex position, int positionIndex) const = 0; /** \brief * Pointer to a function which connects the set of local basis functions * with its global DOFs. * getDOFIndices(el, admin, dof) returns a pointer to a const vector of * length \ref nBasFcts where the i-th entry is the index of the DOF * associated to the i-th basis function; arguments are the actual element * el and the DOF admin admin of the corresponding finite element space * (these indices depend on all defined DOF admins and thus on the * corresponding admin); if the last argument dof is NULL, getDOFndices * has to provide memory for storing this vector, which is overwritten on the * next call of getDOFIndices; if dof is not NULL, dof is a pointer to a * vector which has to be filled; */ virtual const DegreeOfFreedom* getDOFIndices(const Element*, const DOFAdmin&, DegreeOfFreedom*) const = 0; /** \brief * Pointer to a function which fills a vector with the boundary types of the * basis functions; * getBound(el info, bound) returns a pointer to this vector of length * \ref nBasFcts where the i-th entry is the boundary type of the i-th basis * function; bound may be a pointer to a vector which has to be filled * (compare the dof argument of \ref getDOFIindices); * such a function needs boundary information; thus, all routines using this * function on the elements need the FILL_BOUND flag during mesh traversal; */ virtual const BoundaryType* getBound(const ElInfo*, BoundaryType *) const { return NULL; }; /** \brief * Returns \ref degree of BasisFunction */ inline const int getDegree() const { return degree; }; /** \brief * Returns \ref dim of BasisFunction */ inline const int getDim() const { return dim; }; /** \brief * Returns \ref nBasFcts which is the number of local basis functions */ inline const int getNumber() const { return nBasFcts; }; /** \brief * Returns \ref name of BasisFunction */ inline const ::std::string& getName() const { return name; }; /** \brief * Returns \ref nDOF[i] */ int getNumberOfDOFs(int i) const; /** \brief * Returns \ref nDOF */ inline DimVec* getNumberOfDOFs() const { return nDOF; }; /** \brief * Initialisation of the \ref nDOF vector. Must be implemented by sub classes */ virtual void setNDOF() = 0; /** \brief * Returns the barycentric coordinates of the i-th basis function. */ virtual DimVec *getCoords(int i) const = 0; /** \brief * Returns a pointer to a const vector with interpolation coefficients of the * function f; if indices is a pointer to NULL, the coefficient for all * basis functions are calculated and the i-th entry in the vector is the * coefficient of the i-th basis function; if indices is non NULL, only the * coefficients for a subset of the local basis functions has to be * calculated; n is the number of those basis functions, indices[0], . . . * , indices[n-1] are the local indices of the basis functions where the * coefficients have to be calculated, and the i-th entry in the return * vector is then the coefficient of the indices[i]-th basis function; coeff * may be a pointer to a vector which has to be filled * (compare the dof argument of \ref getDOFIndices()); * such a function usually needs vertex coordinate information; thus, all * routines using this function on the elements need the FILL COORDS flag * during mesh traversal. * Must be implemented by sub classes. */ virtual const double* interpol(const ElInfo *el_info, int n, const int *indices, AbstractFunction > *f, double *coeff) = 0; /** \brief * WorldVector valued interpol function. */ virtual const WorldVector* interpol(const ElInfo *el_info, int no, const int *b_no, AbstractFunction,WorldVector > *f, WorldVector *vec) = 0; /** \brief * Returns the i-th local basis function */ inline BasFctType *getPhi(int i) const { return (*phi)[i]; }; /** \brief * Returns the gradient of the i-th local basis function */ inline GrdBasFctType *getGrdPhi(int i) const { return (*grdPhi)[i]; }; /** \brief * Returns the second derivative of the i-th local basis function */ inline D2BasFctType *getD2Phi(int i) const { return (*d2Phi)[i]; }; /** \brief * Approximates the L2 scalar products of a given function with all basis * functions by numerical quadrature and adds the corresponding values to a * DOF vector; * f is a pointer for the evaluation of the given function in world * coordinates x and returns the value of that function at x; if f is a NULL * pointer, nothing is done; * fh is the DOF vector where at the i-th entry the approximation of the L2 * scalar product of the given function with the i-th global basis function * of fh->feSpace is stored; * quad is the quadrature for the approximation of the integral on each leaf * element of fh->feSpace->mesh; if quad is a NULL pointer, a default * quadrature which is exact of degree 2*fh->feSpace->basFcts->degree-2 is * used. * The integrals are approximated by looping over all leaf elements, * computing the approximations to the element contributions and adding * these values to the vector fh by add element vec(). * The vector fh is not initialized with 0.0; only the new contributions are * added */ virtual void l2ScpFctBas(Quadrature*, AbstractFunction >* /*f*/, DOFVector* /*fh*/) {}; /** \brief * WorldVector valued l2ScpFctBas function */ virtual void l2ScpFctBas(Quadrature* , AbstractFunction, WorldVector >* /*f*/, DOFVector >* /*fh*/) {}; /** \brief * Interpolates a DOFIndexed after refinement */ virtual void refineInter(DOFIndexed *, RCNeighbourList*, int){}; /** \brief * Interpolates a DOFIndexed after coarsening */ virtual void coarseInter(DOFIndexed *, RCNeighbourList*, int){}; /** \brief * Restricts a DOFIndexed after coarsening */ virtual void coarseRestr(DOFIndexed *, RCNeighbourList*, int){}; /** \brief * Interpolates a DOFVector > after refinement */ virtual void refineInter(DOFVector >*, RCNeighbourList*, int){}; /** \brief * Interpolates a DOFVector > after coarsening */ virtual void coarseInter(DOFVector >*, RCNeighbourList*, int){}; /** \brief * Restricts a DOFVector > after coarsening */ virtual void coarseRestr(DOFVector >*, RCNeighbourList*, int){}; /** \brief * Returns local dof indices of the element for the given fe space. */ virtual const DegreeOfFreedom *getLocalIndices(const Element*, const DOFAdmin*, DegreeOfFreedom*) const { return NULL; }; /** \brief * Evaluates elements value at barycentric coordinates lambda with local * coefficient vector uh. */ double evalUh(const DimVec& lambda, const double* uh) const;  Thomas Witkowski committed Mar 05, 2008 328 329 330 331 332 333 334 335 336  /** \brief * Evaluates elements value at barycentric coordinates lambda with local * coefficient vector uh. If val is not NULL the result will be stored * there, otherwise a pointer to a static local variable is returned which * will be overwritten after the next call. */ const WorldVector& evalUh(const DimVec& lambda, const WorldVector* uh, WorldVector* val) const;  Peter Gottschling committed Feb 15, 2008 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  /** \brief * Evaluates the gradient at barycentric coordinates lambda. Lambda is the * Jacobian of the barycentric coordinates. uh is the local coefficient * vector. If val is not NULL the result will be stored * there, otherwise a pointer to a static local variable is returned which * will be overwritten after the next call. */ const WorldVector& evalGrdUh(const DimVec& lambda, const DimVec >& Lambda, const double* uh, WorldVector* val) const; /** \brief * Evaluates the second derivative at barycentric coordinates lambda. * Lambda is the Jacobian of the barycentric coordinates. uh is the local * coefficient vector. If val is not NULL the result will be stored * there, otherwise a pointer to a static local variable is returned which * will be overwritten after the next call. */ const WorldMatrix& evalD2Uh(const DimVec& lambda, const DimVec >& Lambda, const double* uh, WorldMatrix* val) const; protected: /** \brief * Textual description */ ::std::string name; /** \brief * Number of basisfunctions on one Element */ int nBasFcts; /** \brief * Maximal degree of the basis functions */ int degree; /** \brief * Dimension of the basis functions */ int dim; /** \brief * Number of DOFs at the different positions */ DimVec *nDOF; /** \brief * Vector of the local functions */ ::std::vector *phi; /** \brief * Vector of gradients */ ::std::vector *grdPhi; /** \brief * Vector of second derivatives */ ::std::vector *d2Phi; }; } #endif // AMDIS_BASISFUNCTION_H