5#ifndef DUNE_HIERARCHICAL_SIMPLEX_P2_WITH_ELEMENT_BUBBLE_LOCALBASIS_HH
6#define DUNE_HIERARCHICAL_SIMPLEX_P2_WITH_ELEMENT_BUBBLE_LOCALBASIS_HH
18#include <dune/localfunctions/common/localbasis.hh>
19#include <dune/localfunctions/common/localkey.hh>
23 template<
class D,
class R,
int dim>
24 class HierarchicalSimplexP2WithElementBubbleLocalBasis
27 HierarchicalSimplexP2WithElementBubbleLocalBasis()
47 template<
class D,
class R>
48 class HierarchicalSimplexP2WithElementBubbleLocalBasis<D,R,1>
63 std::vector<typename Traits::RangeType>& out)
const
69 out[2] = 1-4*(in[0]-0.5)*(in[0]-0.5);
75 std::vector<typename Traits::JacobianType>& out)
const
81 out[2][0][0] = 4-8*in[0];
85 void partial (
const std::array<unsigned int, 1>& order,
87 std::vector<typename Traits::RangeType>& out)
const
89 auto totalOrder = order[0];
90 if (totalOrder == 0) {
91 evaluateFunction(in, out);
92 }
else if (totalOrder == 1) {
97 }
else if (totalOrder == 2) {
104 out[0] = out[1] = out[2] = 0;
138 template<
class D,
class R>
139 class HierarchicalSimplexP2WithElementBubbleLocalBasis<D,R,2>
154 std::vector<typename Traits::RangeType>& out)
const
158 out[0] = 1 - in[0] - in[1];
159 out[1] = 4*in[0]*(1-in[0]-in[1]);
161 out[3] = 4*in[1]*(1-in[0]-in[1]);
162 out[4] = 4*in[0]*in[1];
164 out[6] = 27*in[0]*in[1]*(1-in[0]-in[1]);
171 std::vector<typename Traits::JacobianType>& out)
const
175 out[0][0][0] = -1; out[0][0][1] = -1;
176 out[1][0][0] = 4-8*in[0]-4*in[1]; out[1][0][1] = -4*in[0];
177 out[2][0][0] = 1; out[2][0][1] = 0;
178 out[3][0][0] = -4*in[1]; out[3][0][1] = 4-4*in[0]-8*in[1];
179 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0];
180 out[5][0][0] = 0; out[5][0][1] = 1;
183 out[6][0][0] = 27 * in[1] * (1 - 2*in[0] - in[1]);
184 out[6][0][1] = 27 * in[0] * (1 - 2*in[1] - in[0]);
189 void partial (
const std::array<unsigned int, 2>& order,
191 std::vector<typename Traits::RangeType>& out)
const
194 if (totalOrder == 0) {
195 evaluateFunction(in, out);
196 }
else if (totalOrder == 1) {
198 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
203 out[1] = 4-8*in[0]-4*in[1];
208 out[6] = 27 * in[1] * (1 - 2*in[0] - in[1]);
214 out[3] = 4-4*in[0]-8*in[1];
217 out[6] = 27 * in[0] * (1 - 2*in[1] - in[0]);
261 template<
class D,
class R>
262 class HierarchicalSimplexP2WithElementBubbleLocalBasis<D,R,3>
277 std::vector<typename Traits::RangeType>& out)
const
281 out[0] = 1 - in[0] - in[1] - in[2];
282 out[1] = 4 * in[0] * (1 - in[0] - in[1] - in[2]);
284 out[3] = 4 * in[1] * (1 - in[0] - in[1] - in[2]);
285 out[4] = 4 * in[0] * in[1];
287 out[6] = 4 * in[2] * (1 - in[0] - in[1] - in[2]);
288 out[7] = 4 * in[0] * in[2];
289 out[8] = 4 * in[1] * in[2];
293 out[10] = 81*in[0]*in[1]*in[2]*(1-in[0]-in[1]-in[2]);
298 std::vector<typename Traits::JacobianType>& out)
const
302 out[0][0][0] = -1; out[0][0][1] = -1; out[0][0][2] = -1;
303 out[1][0][0] = 4-8*in[0]-4*in[1]-4*in[2]; out[1][0][1] = -4*in[0]; out[1][0][2] = -4*in[0];
304 out[2][0][0] = 1; out[2][0][1] = 0; out[2][0][2] = 0;
305 out[3][0][0] = -4*in[1]; out[3][0][1] = 4-4*in[0]-8*in[1]-4*in[2]; out[3][0][2] = -4*in[1];
306 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0]; out[4][0][2] = 0;
307 out[5][0][0] = 0; out[5][0][1] = 1; out[5][0][2] = 0;
308 out[6][0][0] = -4*in[2]; out[6][0][1] = -4*in[2]; out[6][0][2] = 4-4*in[0]-4*in[1]-8*in[2];
309 out[7][0][0] = 4*in[2]; out[7][0][1] = 0; out[7][0][2] = 4*in[0];
310 out[8][0][0] = 0; out[8][0][1] = 4*in[2]; out[8][0][2] = 4*in[1];
311 out[9][0][0] = 0; out[9][0][1] = 0; out[9][0][2] = 1;
313 out[10][0][0] = 81 * in[1] * in[2] * (1 - 2*in[0] - in[1] - in[2]);
314 out[10][0][1] = 81 * in[0] * in[2] * (1 - in[0] - 2*in[1] - in[2]);
315 out[10][0][2] = 81 * in[0] * in[1] * (1 - in[0] - in[1] - 2*in[2]);
319 void partial (
const std::array<unsigned int, 3>& order,
321 std::vector<typename Traits::RangeType>& out)
const
324 if (totalOrder == 0) {
325 evaluateFunction(in, out);
326 }
else if (totalOrder == 1) {
328 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
333 out[1] = 4-8*in[0]-4*in[1]-4*in[2];
342 out[10] = 81 * in[1] * in[2] * (1 - 2*in[0] - in[1] - in[2]);
348 out[3] = 4-4*in[0]-8*in[1]-4*in[2];
355 out[10] = 81 * in[0] * in[2] * (1 - in[0] - 2*in[1] - in[2]);
364 out[6] = 4-4*in[0]-4*in[1]-8*in[2];
368 out[10] = 81 * in[0] * in[1] * (1 - in[0] - in[1] - 2*in[2]);
418 static const int numVertices = dim+1;
421 static const int numEdges = (dim+1)*dim / 2;
426 : li(numVertices+numEdges + 1)
443 return numVertices+numEdges + 1;
453 std::vector<Dune::LocalKey> li;
460 class HierarchicalSimplexP2WithElementBubbleLocalInterpolation
465 template<
typename F,
typename C>
466 void interpolate (
const F& f, std::vector<C>& out)
const
468 typename LB::Traits::DomainType x;
469 typename LB::Traits::RangeType y;
474 x[0] = 0.0; x[1] = 0.0; out[0] = f(x);
475 x[0] = 1.0; x[1] = 0.0; out[2] = f(x);
476 x[0] = 0.0; x[1] = 1.0; out[5] = f(x);
479 x[0] = 0.5; x[1] = 0.0; y = f(x);
480 out[1] = y - out[0]*(1-x[0]) - out[2]*x[0];
482 x[0] = 0.0; x[1] = 0.5; y = f(x);
483 out[3] = y - out[0]*(1-x[1]) - out[5]*x[1];
485 x[0] = 0.5; x[1] = 0.5; y = f(x);
486 out[4] = y - out[2]*x[0] - out[5]*x[1];
489 x[0] = 1.0/3; x[1] = 1.0/3; y = f(x);
492 HierarchicalSimplexP2WithElementBubbleLocalBasis<double,double,2> shapeFunctions;
493 std::vector<typename LB::Traits::RangeType> sfValues;
494 shapeFunctions.evaluateFunction(x, sfValues);
497 for (
int i=0; i<6; i++)
498 out[6] -= out[i]*sfValues[i];
A dense n x m matrix.
Definition: fmatrix.hh:117
vector space out of a tensor product of fields.
Definition: fvector.hh:95
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:74
LocalBasisTraits< D, 1, Dune::FieldVector< D, 1 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 1 > > Traits
export type traits for function signature
Definition: hierarchicalsimplexp2withelementbubble.hh:53
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:62
unsigned int order() const
Polynomial order of the shape functions (2, in this case)
Definition: hierarchicalsimplexp2withelementbubble.hh:110
unsigned int size() const
number of shape functions
Definition: hierarchicalsimplexp2withelementbubble.hh:56
void partial(const std::array< unsigned int, 1 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:85
unsigned int size() const
number of shape functions
Definition: hierarchicalsimplexp2withelementbubble.hh:147
unsigned int order() const
Polynomial order of the shape functions (3 in this case)
Definition: hierarchicalsimplexp2withelementbubble.hh:229
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:153
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:170
void partial(const std::array< unsigned int, 2 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:189
LocalBasisTraits< D, 2, Dune::FieldVector< D, 2 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 2 > > Traits
export type traits for function signature
Definition: hierarchicalsimplexp2withelementbubble.hh:144
unsigned int size() const
number of shape functions
Definition: hierarchicalsimplexp2withelementbubble.hh:270
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:276
unsigned int order() const
Polynomial order of the shape functions (4 in this case)
Definition: hierarchicalsimplexp2withelementbubble.hh:380
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:297
void partial(const std::array< unsigned int, 3 > &order, const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate partial derivatives of all shape functions.
Definition: hierarchicalsimplexp2withelementbubble.hh:319
LocalBasisTraits< D, 3, Dune::FieldVector< D, 3 >, R, 1, Dune::FieldVector< R, 1 >, Dune::FieldMatrix< R, 1, 3 > > Traits
export type traits for function signature
Definition: hierarchicalsimplexp2withelementbubble.hh:267
The local finite element needed for the Zou-Kornhuber estimator for Signorini problems.
Definition: hierarchicalsimplexp2withelementbubble.hh:416
size_t size() const
number of coefficients
Definition: hierarchicalsimplexp2withelementbubble.hh:441
const Dune::LocalKey & localKey(size_t i) const
get i'th index
Definition: hierarchicalsimplexp2withelementbubble.hh:447
HierarchicalSimplexP2WithElementBubbleLocalCoefficients()
Standard constructor.
Definition: hierarchicalsimplexp2withelementbubble.hh:425
Describe position of one degree of freedom.
Definition: localkey.hh:24
Default exception for dummy implementations.
Definition: exceptions.hh:263
Default exception class for range errors.
Definition: exceptions.hh:254
Implements a matrix constructed from a given type representing a field and compile-time given number ...
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
void interpolate(const F &f, const GFS &gfs, XG &xg)
interpolation from a given grid function
Definition: interpolate.hh:177
constexpr T accumulate(Range &&range, T value, F &&f)
Accumulate values.
Definition: hybridutilities.hh:279
Dune namespace.
Definition: alignedallocator.hh:13
constexpr std::integral_constant< std::size_t, sizeof...(II)> size(std::integer_sequence< T, II... >)
Return the size of the sequence.
Definition: integersequence.hh:75
Type traits for LocalBasisVirtualInterface.
Definition: localbasis.hh:35
D DomainType
domain type
Definition: localbasis.hh:43