DUNE PDELab (git)

discretegridviewfunction.hh
1// -*- tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 2 -*-
2// vi: set et ts=4 sw=2 sts=2:
3#ifndef DUNE_PDELAB_FUNCTION_DISCRETEGRIDVIEWFUNCTION_HH
4#define DUNE_PDELAB_FUNCTION_DISCRETEGRIDVIEWFUNCTION_HH
5
6#include <array>
7#include <cstdlib>
8#include <vector>
9#include <memory>
10#include <type_traits>
11
15
16#include <dune/localfunctions/common/interfaceswitch.hh>
17
18#include <dune/pdelab/common/jacobiantocurl.hh>
19#include <dune/pdelab/gridfunctionspace/gridfunctionspace.hh>
20#include <dune/pdelab/gridfunctionspace/localfunctionspace.hh>
21#include <dune/pdelab/gridfunctionspace/lfsindexcache.hh>
22
23#include <dune/functions/gridfunctions/gridviewfunction.hh>
24
25namespace std {
27 template<typename T, int N, typename R2>
28 struct common_type<Dune::FieldVector<T,N>, R2>
29 {
31 };
33 template<typename T, int N, typename R2>
34 struct common_type<Dune::FieldVector<T,N>, Dune::FieldVector<R2,N>>
35 {
37 };
38}
39
40namespace Dune {
41namespace PDELab {
42
43template<typename Signature, typename E, template<class> class D, int B,
44 int diffOrder>
45struct DiscreteGridViewFunctionTraits :
46 Functions::Imp::GridFunctionTraits<
47 typename DiscreteGridViewFunctionTraits<Signature,E,D,B,diffOrder-1>::DerivativeSignature
48 ,E,D,B>
49{};
50
51template<typename Signature, typename E, template<class> class D, int B>
52struct DiscreteGridViewFunctionTraits<Signature,E,D,B,0> :
53 Functions::Imp::GridFunctionTraits<Signature,E,D,B>
54{};
55
70template<typename GFS, typename V, int diffOrder = 0>
72{
73public:
74 using GridView = typename GFS::Traits::GridView;
76
77 using Domain = typename EntitySet::GlobalCoordinate;
78 using LocalBasisTraits = typename GFS::Traits::FiniteElementMap::Traits::FiniteElement::Traits::LocalBasisType::Traits;
79 using LocalBasisRange = typename LocalBasisTraits::RangeType;
80 using VectorRange = typename V::ElementType;
81 using ElementaryRange = typename std::common_type<LocalBasisRange, VectorRange>::type;
82
83 using LocalDomain = typename EntitySet::LocalCoordinate;
84 using Element = typename EntitySet::Element;
85
86 using Traits =
87 DiscreteGridViewFunctionTraits<ElementaryRange(Domain), EntitySet,
89
90 using Range = typename Traits::Range; // this is actually either the Range, the Jacobian or Hessian
91
92 using Basis = GFS;
93 using GridFunctionSpace = GFS;
94 using Vector = V;
95
96 class LocalFunction
97 {
99 using LFSCache = LFSIndexCache<LFS>;
100 using XView = typename Vector::template ConstLocalView<LFSCache>;
101
102 public:
103
104 using GlobalFunction = DiscreteGridViewFunction;
105 using Domain = LocalDomain;
106 using Range = GlobalFunction::Range;
107 using Element = GlobalFunction::Element;
108 using size_type = std::size_t;
109
110 LocalFunction(const std::shared_ptr<const GridFunctionSpace> gfs, const std::shared_ptr<const Vector> v)
111 : pgfs_(gfs)
112 , v_(v)
113 , lfs_(*pgfs_)
114 , lfs_cache_(lfs_)
115 , x_view_(*v_)
116 , xl_(pgfs_->maxLocalSize())
117 , yb_(pgfs_->maxLocalSize())
118 , element_(nullptr)
119 {}
120
127 void bind(const Element& element)
128 {
129 element_ = &element;
130 lfs_.bind(element);
131 lfs_cache_.update();
132 x_view_.bind(lfs_cache_);
133 x_view_.read(xl_);
134 x_view_.unbind();
135 }
136
137 void unbind()
138 {
139 element_ = nullptr;
140 }
141
142 const Element& localContext() const
143 {
144#ifndef NDEBUG
145 if (!element_)
146 DUNE_THROW(InvalidStateException,"can't call localContext on unbound DiscreteGridViewFunction::LocalFunction");
147#endif
148 return *element_;
149 }
150
166 friend typename DiscreteGridViewFunction<GFS,V,diffOrder+1>::LocalFunction derivative(const LocalFunction& t)
167 {
169 diff(t.pgfs_, t.v_);
170 // TODO: do we really want this?
171 if (t.element_) diff.bind(*t.element_);
172 return diff;
173 }
174
184 Range
185 operator()(const Domain& coord) const
186 {
187 return evaluate<diffOrder>(coord);
188 };
189
190 private:
191 template<int dOrder>
192 typename std::enable_if<(dOrder > 2),
193 Range>::type
194 evaluate(const Domain& coord) const
195 {
196 if (diffOrder > 2) DUNE_THROW(NotImplemented,
197 "Derivatives are only implemented up to degree 2");
198 };
199
200 template<int dOrder>
201 typename std::enable_if<dOrder == 0,
202 Range>::type
203 evaluate(const Domain& coord) const
204 {
205 Range r(0);
206 auto& basis = lfs_.finiteElement().localBasis();
207 basis.evaluateFunction(coord,yb_);
208 for (size_type i = 0; i < yb_.size(); ++i)
209 {
210 r.axpy(xl_[i],yb_[i]);
211 }
212 return r;
213 }
214
215 template<int dOrder>
216 typename std::enable_if<dOrder == 1,
217 Range>::type
218 evaluate(const Domain& coord) const
219 {
220 Range r(0);
221 // get Jacobian of geometry
222 const typename Element::Geometry::JacobianInverseTransposed
223 JgeoIT = element_->geometry().jacobianInverseTransposed(coord);
224
225 // get local Jacobians/gradients of the shape functions
226 lfs_.finiteElement().localBasis().evaluateJacobian(coord,yb_);
227
228 Range gradphi;
229 r = 0;
230 for(std::size_t i = 0; i < yb_.size(); ++i) {
231 assert(gradphi.size() == yb_[i].size());
232 for(std::size_t j = 0; j < gradphi.size(); ++j) {
233 // compute global gradient of shape function i
234 // graphi += {J^{-1}}^T * yb_i0
235 JgeoIT.mv(yb_[i][j], gradphi[j]);
236
237 // sum up global gradients, weighting them with the appropriate coeff
238 // r \in R^{1,dim}
239 // r_0 += xl_i * grad \phi
240 r[j].axpy(xl_[i], gradphi[j]);
241 }
242 }
243 return r;
244 }
245
246 template<int dOrder>
247 typename std::enable_if<dOrder == 2,
248 Range>::type
249 evaluate(const Domain& coord) const
250 {
251 Range r(0);
252 // TODO: we currently require affine geometries.
253 if (! element_->geometry().affine())
254 DUNE_THROW(NotImplemented, "Due to missing features in the Geometry interface, "
255 "the computation of higher derivatives (>=2) works only for affine transformations.");
256 // get Jacobian of geometry
257 const typename Element::Geometry::JacobianInverseTransposed
258 JgeoIT = element_->geometry().jacobianInverseTransposed(coord);
259
260 // TODO: we currently only implement the hessian...
261 // a proper implementation will require TMP magic.
262 static const unsigned int dim = GridView::dimensionworld;
263 // static_assert(
264 // isHessian<Range>::value,
265 // "Currently the only higher order derivative we support is the Hessian of scalar functions");
266
267 // get local hessian of the shape functions
268 std::array<std::size_t, dim> directions;
269 for(std::size_t i = 0; i < dim; ++i) {
270 // evaluate diagonal entries
271 directions[i] = 2;
272 // evaluate offdiagonal entries
273 directions[i] = 1;
274 for(std::size_t j = i+1; j < dim; ++j) {
275 directions[j] = 1;
276 lfs_.finiteElement().localBasis().partial(directions,coord,yb_);
277 assert( yb_.size() == 1); // TODO: we only implement the hessian of scalar functions
278 for(std::size_t n = 0; n < yb_.size(); ++n) {
279 // sum up derivatives, weighting them with the appropriate coeff
280 r[i][j] += xl_[i] * yb_[j];
281 }
282 // use symmetry of the hessian
283 r[j][i] = r[i][j];
284 directions[j] = 0;
285 }
286 directions[i] = 0;
287 }
288 // transform back to global coordinates
289 for(std::size_t i = 0; i < dim; ++i)
290 for(std::size_t j = i; j < dim; ++j)
291 r[i][j] *= JgeoIT[i][j] * JgeoIT[i][j];
292 return r;
293 }
294
295 protected:
296
297 const std::shared_ptr<const GridFunctionSpace> pgfs_;
298 const std::shared_ptr<const Vector> v_;
299 LFS lfs_;
300 LFSCache lfs_cache_;
301 XView x_view_;
302 mutable std::vector<ElementaryRange> xl_;
303 mutable std::vector<Range> yb_;
304 const Element* element_;
305 };
306
307 DiscreteGridViewFunction(const GridFunctionSpace& gfs, const Vector& v)
309 {}
310
311 DiscreteGridViewFunction(std::shared_ptr<const GridFunctionSpace> pgfs, std::shared_ptr<const Vector> v)
312 : pgfs_(pgfs),v_(v)
313 {}
314
315 // this is part of the interface in dune-functions
316 const Basis& basis() const
317 {
318 return *pgfs_;
319 }
320 const GridFunctionSpace& gridFunctionSpace() const
321 {
322 return *pgfs_;
323 }
324
325 const V& dofs() const
326 {
327 return *v_;
328 }
329
332 {
333 return pgfs_;
334 }
335
337 auto dofsStorage() const
338 {
339 return v_;
340 }
341
342 // TODO: Implement this using hierarchic search
343 Range operator() (const Domain& x) const
344 {
345 DUNE_THROW(NotImplemented,"not implemented");
346 }
347
348 friend DiscreteGridViewFunction<GFS,V,diffOrder+1> derivative(const DiscreteGridViewFunction& t)
349 {
350 return DiscreteGridViewFunction<GFS,V,diffOrder+1>(t.pgfs_, t.v_);
351 }
352
362 friend LocalFunction localFunction(const DiscreteGridViewFunction& t)
363 {
364 return LocalFunction(t.pgfs_, t.v_);
365 }
366
371 {
372 return pgfs_->gridView();
373 }
374
375private:
376
377 const std::shared_ptr<const GridFunctionSpace> pgfs_;
378 const std::shared_ptr<const Vector> v_;
379
380};
381
382} // end of namespace Dune::PDELab
383} // end of namespace Dune
384
385#endif // DUNE_PDELAB_FUNCTION_DISCRETEGRIDVIEWFUNCTION_HH
vector space out of a tensor product of fields.
Definition: fvector.hh:91
GridView::template Codim< codim >::Entity Element
Type of Elements contained in this EntitySet.
Definition: gridviewentityset.hh:36
Element::Geometry::LocalCoordinate LocalCoordinate
Type of local coordinates with respect to the Element.
Definition: gridviewentityset.hh:39
Default exception if a function was called while the object is not in a valid state for that function...
Definition: exceptions.hh:281
Default exception for dummy implementations.
Definition: exceptions.hh:263
A discrete function defined over a GridFunctionSpace.
Definition: discretegridviewfunction.hh:72
EntitySet entitySet() const
Get associated EntitySet.
Definition: discretegridviewfunction.hh:370
auto dofsStorage() const
Returns storage object of the dof storage vector.
Definition: discretegridviewfunction.hh:337
friend LocalFunction localFunction(const DiscreteGridViewFunction &t)
Get local function of wrapped function.
Definition: discretegridviewfunction.hh:362
auto gridFunctionSpaceStorage() const
Returns storage object of the grid function space.
Definition: discretegridviewfunction.hh:331
A few common exception classes.
Implements a vector constructed from a given type representing a field and a compile-time given size.
#define DUNE_THROW(E, m)
Definition: exceptions.hh:218
static constexpr int dimensionworld
The dimension of the world the grid lives in.
Definition: gridview.hh:137
Dune namespace.
Definition: alignedallocator.hh:13
std::shared_ptr< T > stackobject_to_shared_ptr(T &t)
Create a shared_ptr for a stack-allocated object.
Definition: shared_ptr.hh:72
STL namespace.
This file implements several utilities related to std::shared_ptr.
Default implementation for derivative traits.
Definition: defaultderivativetraits.hh:41
R RangeType
range type
Definition: localbasis.hh:52
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