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 Praetorius, Simon committed Apr 14, 2020 1 2 3 4 5 # 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)  Müller, Felix committed Sep 29, 2020 6 into a [GridFunction](../GridFunctions) that allows to use it like a function defined on a grid.  Praetorius, Simon committed Apr 14, 2020 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  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  Müller, Felix committed Sep 29, 2020 26 Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/amdis/DOFVector.hpp)  Praetorius, Simon committed Apr 14, 2020 27 28 29 30  c++ template >  Praetorius, Simon committed Apr 14, 2020 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 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 [backup](#function-dofvectorbackup) | Write DOFVector to file [restore](#function-dofvectorrestore) | Read backup data from file [dataTransfer](#function-dofvectordataTransfer) | Return the associated DataTransfer object  Müller, Felix committed Sep 30, 2020 62 ??? seealso "Functions inherited from [VectorFacade](../MatVecFacade/#class-vectorfacade)"  Praetorius, Simon committed Apr 14, 2020 63 64  Function | Descriptions --------------------------------|---------------------------------------------  Müller, Felix committed Sep 30, 2020 65 66 67 68 69 70 71 72 73 74  [impl](../MatVecFacade#function-vectorbasebackend) | Return the backend vector wrapper implementing the actual algebra [localSize,globalSize](../MatVecFacade#function-vectorbasesize) | The number of entries in the local part of the vector [resize,resizeZero](../MatVecFacade#function-vectorbaseglobalSize)| Resize the vector to the size of the basis [init](../MatVecFacade#function-vectorbaseglobalSize) | Prepare the vector for insertion of values [finish](../MatVecFacade#function-vectorbaseglobalSize) | Finish the insertion of values [at](../MatVecFacade#function-vectorbaseat) | Return the value of the vector at the given local index [insert,set,add](../MatVecFacade#function-vectorbaseinsert) | Insert a single value into the matrix [gather](../MatVecFacade#function-vectorbasegather) | Extract values from the vector referring to the given local indices [scatter](../MatVecFacade#function-vectorbasescatter) | Insert a block of values into the vector [forEach](../MatVecFacade#function-vectorbasescatter) | Apply a functor to each value at given indices  Praetorius, Simon committed Apr 14, 2020 75 76 77 78 79 80  ## function DOFVector::DOFVector c++ template DOFVector(Basis&& basis, DataTransferOperation op = INTERPOLATE)  Müller, Felix committed Sep 30, 2020 81 82 83  template DOFVector(GV const& gridView, PBF const& preBasisFactory, DataTransferOperation op = INTERPOLATE)  Praetorius, Simon committed Apr 14, 2020 84 85   Müller, Felix committed Sep 30, 2020 86 Constructs the DOFVector from a given global basis or a grid view and a basis factory, and optionally a DataTransferOperation that defines how the DOFVector is handled during grid adaption.  Praetorius, Simon committed Apr 14, 2020 87 88 89  #### Arguments Basis basis  Müller, Felix committed Sep 30, 2020 90 91 92 93 94 95 96 : Either a shared_ptr to the GlobalBasis type or anything that can be converted to that, e.g. a reference or a unique_ptr. References to lvalues are wrapped into non-destroying shared_ptrs whereas rvalue-references are moved into new basis objects. GV gridView : A grid view provided by the grid PBF preBasisFactory : A factory to create a pre-basis, see [the ref page on GlobalBasis](../GlobalBasis#making-a-prebasis)  Praetorius, Simon committed Apr 14, 2020 97 98 99 100 101 102 103 104 105 106  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;  Praetorius, Simon committed Nov 07, 2020 107 GlobalBasis basis1(grid.leafGridView(), lagrange<2>());  Praetorius, Simon committed Apr 14, 2020 108 109 110 111  DOFVector vec0(basis1); DOFVector vec1(basis1); // C++17 only  Praetorius, Simon committed Nov 07, 2020 112 auto basis2 = makeUniquePtr(GlobalBasis{grid.leafGridView(), lagrange<2>()});  Praetorius, Simon committed Apr 14, 2020 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 DOFVector> vec2(std::move(basis2));  #### See Also - Generator function to construct a DOFVector: [makeDOFVector()](#function-makedofvector) ## 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 makeDOFVector  Müller, Felix committed Sep 29, 2020 146 Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/amdis/DOFVector.hpp)  Praetorius, Simon committed Apr 14, 2020 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164  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  Praetorius, Simon committed Nov 07, 2020 165 : Reference, temporary, or shared_ptr to dune global basis or GlobalBasis  Praetorius, Simon committed Apr 14, 2020 166 167 168 169 170 171 172 173 174  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  Praetorius, Simon committed Nov 07, 2020 175 Returns a DOFVector with GB = GlobalBasis::PreBasis>. The  Praetorius, Simon committed Apr 14, 2020 176 177 178 179 180 181 182 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  Praetorius, Simon committed Nov 07, 2020 183 GlobalBasis basis1(gridView, lagrange<2>());  Praetorius, Simon committed Apr 14, 2020 184 185 186 187 188 189 190 191 192 auto vec1 = makeDOFVector(basis1); // pass a smart pointer auto basis2 = std::make_shared(basis1); auto vec2 = makeDOFVector(basis2, DataTransferOperation::NO_OPERATION);  ## class DiscreteFunction  Müller, Felix committed Sep 29, 2020 193 Defined in header [](https://gitlab.mn.tu-dresden.de/amdis/amdis-core/blob/master/amdis/gridfunctions/DiscreteFunction.hpp)  Praetorius, Simon committed Apr 14, 2020 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  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)  Müller, Felix committed Sep 30, 2020 248 DiscreteFunction(DOFVector const& dofVector, GlobalBasis const& basis,  Praetorius, Simon committed Apr 14, 2020 249 250  TreePath const& treePath = {}) // (2)  Müller, Felix committed Sep 30, 2020 251 DiscreteFunction(DOFVector& dofVector, GlobalBasis const& basis,  Praetorius, Simon committed Apr 14, 2020 252 253 254 255 256 257 258 259 260 261 262  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.  Müller, Felix committed Sep 30, 2020 263 264 265 GlobalBasis const& basis : The global basis associated with the dofvector.  Praetorius, Simon committed Apr 14, 2020 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 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. ## 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)  Praetorius, Simon committed Oct 14, 2020 307 308 template auto child(Indices... ii) const  Praetorius, Simon committed Apr 14, 2020 309 310  // (2)  Praetorius, Simon committed Oct 14, 2020 311 312 template auto child(Indices... ii)  Praetorius, Simon committed Apr 14, 2020 313 314 315 316 317  Returns the const (1) or mutable (2) sub-range view of the stored DOFVector. #### Arguments  Praetorius, Simon committed Oct 14, 2020 318 319 Indices... ii : Components of the tree-path identifying a node in the basis tree.  Praetorius, Simon committed Apr 14, 2020 320 321 322  #### Example c++  Praetorius, Simon committed Nov 07, 2020 323 GlobalBasis basis{gridView, power<3>(lagrange<1>())};  Praetorius, Simon committed Apr 14, 2020 324 auto vec = makeDOFVector(basis);  Praetorius, Simon committed Nov 05, 2020 325 auto df = valueOf(vec);  Praetorius, Simon committed Apr 14, 2020 326 327 328 329  auto df1 = df.child(); auto df2 = df.child(0); auto df3 = df.child(_0);  Praetorius, Simon committed Nov 05, 2020 330 331 auto df4 = valueOf(df,0); auto df5 = valueOf(vec,0); // df4 == df5  Praetorius, Simon committed Apr 14, 2020 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354  ## 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  Müller, Felix committed Sep 30, 2020 355 DiscreteFunction& operator-=(Expr&& expr)  Praetorius, Simon committed Apr 14, 2020 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  (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++  Praetorius, Simon committed Nov 07, 2020 386 GlobalBasis basis{gridView, power<3>(lagrange<1>())};  Praetorius, Simon committed Apr 14, 2020 387 388 389 auto vec = makeDOFVector(basis); // Range type is FieldVector  Praetorius, Simon committed Nov 05, 2020 390 valueOf(vec) << [](FieldVector const& x) -> FieldVector { return x; };  Praetorius, Simon committed Apr 14, 2020 391 392  // Range type is double  Praetorius, Simon committed Nov 05, 2020 393 valueOf(vec,0) += 42.0;  Praetorius, Simon committed Apr 14, 2020 394