DOFVector.md 19.9 KB
 Praetorius, Simon committed Apr 14, 2020 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 # DOFVector and DiscreteFunction {: #group-dofvector } ## Summary The class [DOFVector](#class-dofvector) acts as a container for storing the coefficients of the solution discrete function. It is attached to a global basis to give its coefficients a meaning. A [DiscreteFunction](#class-discretefunction) goes one step further and transforms a DOFVector or subspaces of a DOFVector (with respecto to a sub basis) into a [GridFunction](/reference/GridFunctions) that allows to use it like a function defined on a grid. Let $\{\phi_i\}$ be the set of basis functions of a finite-element space $V$. A function $u\in V$ can be represented as math u(\mathbf{x}) = \sum_i u_i \phi_i(\mathbf{x})  with coefficients $(u_i)$. The pair $\{(u_i),\{\phi_i\}\}$ is called DOFVector and the function $u=u(\mathbf{x})$ is called DiscreteFunction. ### Classes Class | Descriptions --------------------------------|--------------------------------------------- [DOFVector](#class-dofvector) | Standard container for storing solution coefficients associated to a functionspace basis [DiscreteFunction](#class-discretefunction) | Wrapper that transforms a DOFVector into a GridFunction ## class DOFVector Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/src/amdis/DOFVector.hpp) c++ template > class DOFVector : public VectorFacade  DOFVector is a vector data-structure for the coefficients of a discrete function associated to a GlobalBasis GB. The template parameter GB defines the global basis type and T the value type of the coefficients in the vector. It defaults to double. The third parameter Traits is a collection of parameters characterizing the Linear-Algebra backend. It defaults to the default backend Traits. ### Member Types Member Type | Definition --------------------------------|--------------------------------------------- GlobalBasis | GB Traits | Traits size_type | typename GlobalBasis::size_type value_type | typename Backend::value_type The value_type is often the same as T, but might be just something similar, like PetscScalar. ### Member functions Function | Descriptions --------------------------------|--------------------------------------------- [*(constructor)*](#function-dofvectordofvector) | Construct the DOFVector [child](#function-dofvectorchild) | Return a DiscreteFunction of a given sub-space [backup](#function-dofvectorbackup) | Write DOFVector to file [restore](#function-dofvectorrestore) | Read backup data from file [dataTransfer](#function-dofvectordataTransfer) | Return the associated DataTransfer object ### Interpolation functions Function | Descriptions --------------------------------|--------------------------------------------- [interpolate](#function-dofvectorinterpolate) | Interpolation of GridFunction to DOFVector [interpolate_noalias](#function-dofvectorinterpolate) | Interpolation of GridFunction to DOFVector assuming no aliasing [operator<<](#function-dofvectorinterpolate) | Operator for the interpolation ??? seealso "Functions inherited from [VectorFacade](/reference/MatVecBase/#class-vectorfacade)" Function | Descriptions --------------------------------|--------------------------------------------- [basis](/reference/MatVecBase#function-vectorbasebasis) | Return the GlobalBasis associated with the vector [backend](/reference/MatVecBase#function-vectorbasebackend) | Return the backend vector wrapper implementing the actual algebra [localSize,globalSize](/reference/MatVecBase#function-vectorbasesize) | The number of entries in the local part of the vector [resize,resizeZero](/reference/MatVecBase#function-vectorbaseglobalSize)| Resize the vector to the size of the basis [init](/reference/MatVecBase#function-vectorbaseglobalSize) | Prepare the vector for insertion of values [finish](/reference/MatVecBase#function-vectorbaseglobalSize) | Finish the insertion of values [at](/reference/MatVecBase#function-vectorbaseat) | Return the value of the vector at the given local index [insert,set,add](/reference/MatVecBase#function-vectorbaseinsert) | Insert a single value into the matrix [gather](/reference/MatVecBase#function-vectorbasegather) | Extract values from the vector referring to the given local indices [scatter](/reference/MatVecBase#function-vectorbasescatter) | Insert a block of values into the vector [copy](/reference/MatVecBase#function-vectorbasescatter) | Copies a block of values into the vector [forEach](/reference/MatVecBase#function-vectorbasescatter) | Apply a functor to each value at given indices ## function DOFVector::DOFVector c++ template DOFVector(Basis&& basis, DataTransferOperation op = INTERPOLATE)  Constructs the DOFVector from a given global basis and optionally a DataTransferOperation that defines how the DOFVector is handled during grid adaption. #### Arguments Basis basis : Either a shared_ptr to the GlobalBasis type or anything that can be converted to that, e.g. a reference or a unique_ptr or a dune-functions DefaultGlobalBasis. References to lavlues are wrapped into non-destroying shared_ptrs whereas rvalue-references are moved into new basis objects. DataTransferOperation op : The operation performed during data-transfer, either DataTransferOperation::INTERPOLATE or DataTransferOperation::NO_OPERATION #### Example c++ using Grid = Dune::YaspGrid<2>; Grid grid({1.0, 1.0}, {2, 2}); using namespace Dune::Functions::BasisFactory;  Müller, Felix committed Aug 06, 2020 112 ParallelGlobalBasis basis1(grid.leafGridView(), lagrange<2>());  Praetorius, Simon committed Apr 14, 2020 113 114 115 116  DOFVector vec0(basis1); DOFVector vec1(basis1); // C++17 only  Müller, Felix committed Aug 06, 2020 117 auto basis2 = makeUniquePtr(ParallelGlobalBasis(grid.leafGridView(), lagrange<2>()));  Praetorius, Simon committed Apr 14, 2020 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 DOFVector> vec2(std::move(basis2));  #### See Also - Generator function to construct a DOFVector: [makeDOFVector()](#function-makedofvector) ## function DOFVector::child c++ template auto child(TreePath const& path = {}) // (1) template auto child(TreePath const& path = {}) const // (2)  (1) Creates a mutable DiscreteFunction representing the sub-space w.r.t. the passed tree-path. The path thereby refers to the hierarchic global basis. (2) Creates a constant DiscreteFunction representing the sub-space w.r.t. the passed tree-path. The path thereby refers to the hierarchic global basis. #### Arguments TreePath path : A Treepath identifying a node in the basis tree. #### Example c++ DOFVector vec(basis); auto vec_ = vec.child(); auto vec_0 = vec.child(_0); auto vec_10 = vec.child(treepath(_1,0));  ## function DOFVector::backup c++ void backup(std::string const& filename);  Writes the coefficients of the DOFVector to file. Thereby the data is first extracted element-wise and then written using binary ofstreams. #### Arguments std::string filename : The filename of the backup file that is created. ## function DOFVector::restore c++ void restore(std::string const& filename);  Reads a backup of the DOFVector from file previously created using the [backup()](#function-dofvectorbackup) function. #### Arguments std::string filename : The filename of the backup file to read from. ## function DOFVector::interpolate,interpolate_noalias,operator<< {: #function-dofvectorinterpolate } c++ // (1) template void interpolate_noalias(Expr&& expr, Tag strategy) // (2) template void interpolate(Expr&& expr, Tag strategy) // (3) template DOFVector& operator<<(Expr&& expr)  (1) Interpolation of a GridFunction (or Expression) to the DOFVector, assuming that there is no reference to this DOFVector in the expression (no aliasing). (2) Interpolation of a GridFunction (or Expression) to the DOFVector, allowing aliasing. (3) Operator notation of (2) using averaging strategy. In case *aliasing* is allowed, a temporary DOFVector is created first as copy of *this* and the interpolation performed on the temporary using *noalias* interpolation (1). Then, this tempoary is moved back to *this*. #### Arguments Expr expr : An Expression representing a GridFunction Tag strategy : An interpolation strategy, either tag::average or tag::assign. The average strategy accumulates interpolation values on each dof and takes the average by dividing by the number of assignees. The assign strategy diretly assigns an interpolation value to a dof that might be overwritten in a subsequent interpolation step. ## function makeDOFVector Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/src/amdis/DOFVector.hpp) c++ template DOFVector<...> makeDOFVector(Basis&& basis, DataTransferOperation op = INTERPOLATE)  Creates a DOFVector from a basis. This generator function accepts the basis as reference, temporary, or shared_ptr. Internally the reference is wrapped into a non-destroying shared_ptr and the temporary is moved into a new shared_ptr, see [DOFVector::DOFVector](#function-dofvectordofvector). The DataTransferOperation controls what is done during grid changes with the DOFVector. The default is interpolation of the data to the new grid. #### Arguments Basis basis : Reference, temporary, or shared_ptr to dune global basis or ParallelGlobalBasis DataTransferOperation op : The operation performed during data-transfer, either DataTransferOperation::INTERPOLATE or DataTransferOperation::NO_OPERATION #### Template types T : The type of the coefficients to store in the DOFVector #### Return value Returns a DOFVector with GlobalBasis = ParallelGlobalBasis::PreBasis>. The underlying type is either the remove_cvref_t for references, or the pointed-to type for smart pointers. #### Example c++ using namespace Dune::Functions::BasisFactory; // pass a reference to the basis  Müller, Felix committed Aug 06, 2020 254 ParallelGlobalBasis basis1(gridView, lagrange<2>());  Praetorius, Simon committed Apr 14, 2020 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 auto vec1 = makeDOFVector(basis1); // pass a smart pointer auto basis2 = std::make_shared(basis1); auto vec2 = makeDOFVector(basis2, DataTransferOperation::NO_OPERATION);  ## class DiscreteFunction Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/src/amdis/gridfunctions/DiscreteFunction.hpp) c++ template class DiscreteFunction  A DiscreteFunction is the interpretation of a DOFVector as grid function. ### Template parameters Coefficients : Type of the coefficient vector GlobalBasis : The type of the global basis associated with the DOFVector TreePath : The path in the basis tree representing the subspace represented by this DiscreteFunction ### Member Types Member Type | Definition ---------------------|--------------------------------------------- EntitySet | Set of entities the DiscreteFunction is defined on, GridViewEntitySet Domain | Global coordinates of the EntitySet Range | Range type of this DiscreteFunction, given by sub-tree and coefficient type ### Member functions of the const DiscreteFunction Function | Descriptions --------------------------------|--------------------------------------------- [*(constructor)*](#function-discretefunctiondiscretefunction) | Construct the const DiscreteFunction [entitySet](#function-discretefunctionentityset) | Return the stored GridViewEntitySet [basis](#function-discretefunctionbasis) | Return global basis bound to the DOFVector [treePath](#function-discretefunctiontreepath) | Return the treePath associated with this discrete function [coefficients](#function-discretefunctioncoefficients) | Return const coefficient vector [child](#function-discretefunctionchild) | Return the sub-range view of this DiscreteFunction ### Member functions of the mutable DiscreteFunction Function | Descriptions --------------------------------|--------------------------------------------- [*(constructor)*](#function-discretefunctiondiscretefunction) | Construct the mutable DiscreteFunction [interpolate_noalias](#function-discretefunctioninterpolate) | Interpolation of GridFunction to DOFVector assuming no aliasing [interpolate](#function-discretefunctioninterpolate) | Interpolation of GridFunction to DOFVector [operator<<](#function-discretefunctioninterpolate) | Interpolation of GridFunction to DOFVector [operator+=](#function-discretefunctioninterpolate) | Accumulated interpolation of GridFunction to DOFVector [operator-=](#function-discretefunctioninterpolate) | Accumulated interpolation of GridFunction to DOFVector ## function DiscreteFunction::DiscreteFunction c++ // (1) DiscreteFunction(DOFVector const& dofVector, TreePath const& treePath = {}) // (2) DiscreteFunction(DOFVector& dofVector, TreePath const& treePath = {})  Construction of a DiscreteFunction from a const (1) or mutable (2) DOFVector. The corresponding constructor is only available for the const or mutable is_const template parameter specialization. #### Arguments DOFVector<...> dofvector : The container storing the global coefficients. Is stored as pointer in the DiscreteFunction and thus must have a longer lifetime than the DiscreteFunction. TreePath treePath : A Dune::TypeTree::HybridTreePath<...> representing the coordinates of a node in the basis tree this DiscreteFunction is defined on. The type of the treePath also defines the Range type of the DiscreteFunction. #### See Also - Generator function to construct a DiscreteFunction: [makeDiscreteFunction()](#function-makediscretefunction) ## function DiscreteFunction::entitySet c++ EntitySet const& entitySet() const  Returns a Dune::Functions::GridViewEntitySet of the GridView associated to the GlobalBasis. ## function DiscreteFunction::basis c++ std::shared_ptr basis() const  Returns the global basis bound to the DOFVector. ## function DiscreteFunction::treePath c++ TreePath const& treePath() const  Returns the treePath associated with this DiscreteFunction. ## function DiscreteFunction::coefficients c++ DOFVector const& coefficients() const // (1) DOFVector& coefficients() // (2)  Returns the const (1) or mutable (2) coefficient vector. ## function DiscreteFunction::child c++ // (1) template auto child(TreePath const& path = {}) const // (2) template auto child(TreePath const& path = {})  Returns the const (1) or mutable (2) sub-range view of the stored DOFVector. #### Arguments TreePath path : A Treepath identifying a node in the basis tree. #### Example c++  Müller, Felix committed Aug 06, 2020 394 ParallelGlobalBasis basis(gridView, power<3>(lagrange<1>()));  Praetorius, Simon committed Apr 14, 2020 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 auto vec = makeDOFVector(basis); auto df = makeDiscreteFunction(vec); auto df1 = df.child(); auto df2 = df.child(0); auto df3 = df.child(_0);  ## function DiscreteFunction::interpolate* {: #function-discretefunctioninterpolate } c++ // (1) template void interpolate_noalias(Expr&& expr, Tag strategy) // (2) template void interpolate(Expr&& expr, Tag strategy) // (3) template DiscreteFunction& operator<<(Expr&& expr) // (4) template DiscreteFunction& operator+=(Expr&& expr) // (5) template DiscreteFunction& operator+=(Expr&& expr)  (1) Interpolation of a GridFunction (or Expression) to the subtree of the DOFVector, assuming that there is no reference to this DOFVector in the expression (no aliasing). (2) Interpolation of a GridFunction (or Expression) to the subtree of the DOFVector, allowing aliasing. (3) Operator notation of (2) using averaging strategy. (4) Interpolate (*this) + expr to the subtree of the DOFVector. (5) Interpolate (*this) - expr to the subtree of the DOFVector. In case *aliasing* is allowed, a temporary DOFVector is created first as copy of *this* and the interpolation performed on the temporary using *noalias* interpolation (1). Then, this tempoary is moved back to *this*. Note, the range type of the expression must be compatible with the Range type of the DiscreteFunction. #### Arguments Expr expr : An Expression representing a GridFunction Tag strategy : An interpolation strategy, either tag::average or tag::assign. The average strategy accumulates interpolation values on each dof and takes the average by divising through the number of assignees. The assign strategy diretly assigns an interpolation value to a dof that might be overwritten in a subsequent interpolation step. #### Example c++  Müller, Felix committed Aug 06, 2020 455 ParallelGlobalBasis basis(gridView, power<3>(lagrange<1>()));  Praetorius, Simon committed Apr 14, 2020 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 auto vec = makeDOFVector(basis); auto df1 = vec.child(); auto df2 = vec.child(0); // Range type is FieldVector df1 << [](FieldVector const& x) -> FieldVector { return x; }; // Range type is double df2 += 42.0;  ## function makeDiscreteFunction Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/src/amdis/gridfunctions/DiscreteFunction.hpp) c++ // (1) template > auto makeDiscreteFunction(DOFVector const& dofVector, PreTreePath const& preTreePath = {}) // (2) template > auto makeDiscreteFunction(DOFVector& dofVector, PreTreePath const& preTreePath = {})  Constructs a const (1) or mutable (2) DiscreteFunction from a DOFVector and a tree path. The TreePath can therby by given by a pree-tree path, i.e. a sequence of integers or integral constants a Dune::TypeTree::HybridTreePath can be constructed from. #### Arguments DOFVector<...> dofVector : The container storing the global coefficients. Is stored as pointer in the DiscreteFunction and thus must have a longer lifetime than the DiscreteFunction. PreTreePath preTreePath : A pree-tree path, a Dune::TypeTree::HybridTreePath<...> can be created from. #### Return value Returns a DiscreteFunction if the DOFVector is const, or a DiscreteFunction if the DOFVector is mutable. The TREE_PATH is thereby given by the type of makeTreePath(preTreePath). #### Example c++ using namespace Dune::Functions::BasisFactory; // pass a reference to the basis  Müller, Felix committed Aug 06, 2020 507 ParallelGlobalBasis basis(gridView, power<2>(lagrange<2>()));  Praetorius, Simon committed Apr 14, 2020 508 509 510 511 512 513 514 auto vec = makeDOFVector(basis1); auto df1 = makeDiscreteFunction(vec); auto df2 = makeDiscreteFunction(vec, 1); auto df3 = makeDiscreteFunction(vec, _1); auto df4 = makeDiscreteFunction(vec, Dune::TypeTree::hybridTreePath(0));