5#ifndef DUNE_HIERARCHICAL_SIMPLEX_P2_WITH_ELEMENT_BUBBLE_LOCALBASIS_HH
6#define DUNE_HIERARCHICAL_SIMPLEX_P2_WITH_ELEMENT_BUBBLE_LOCALBASIS_HH
15#include <dune/common/fvector.hh>
16#include <dune/common/fmatrix.hh>
24 template<
class D,
class R,
int dim>
30 DUNE_THROW(Dune::NotImplemented,
"HierarchicalSimplexP2LocalBasis not implemented for dim > 3.");
48 template<
class D,
class R>
64 std::vector<typename Traits::RangeType>& out)
const
70 out[2] = 1-4*(in[0]-0.5)*(in[0]-0.5);
76 std::vector<typename Traits::JacobianType>& out)
const
82 out[2][0][0] = 4-8*in[0];
86 void partial (
const std::array<unsigned int, 1>& order,
88 std::vector<typename Traits::RangeType>& out)
const
90 auto totalOrder = order[0];
91 if (totalOrder == 0) {
92 evaluateFunction(in, out);
93 }
else if (totalOrder == 1) {
98 }
else if (totalOrder == 2) {
105 out[0] = out[1] = out[2] = 0;
138 template<
class D,
class R>
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
193 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
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]);
220 DUNE_THROW(RangeError,
"Component out of range.");
223 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
260 template<
class D,
class R>
276 std::vector<typename Traits::RangeType>& out)
const
280 out[0] = 1 - in[0] - in[1] - in[2];
281 out[1] = 4 * in[0] * (1 - in[0] - in[1] - in[2]);
283 out[3] = 4 * in[1] * (1 - in[0] - in[1] - in[2]);
284 out[4] = 4 * in[0] * in[1];
286 out[6] = 4 * in[2] * (1 - in[0] - in[1] - in[2]);
287 out[7] = 4 * in[0] * in[2];
288 out[8] = 4 * in[1] * in[2];
292 out[10] = 81*in[0]*in[1]*in[2]*(1-in[0]-in[1]-in[2]);
297 std::vector<typename Traits::JacobianType>& out)
const
301 out[0][0][0] = -1; out[0][0][1] = -1; out[0][0][2] = -1;
302 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];
303 out[2][0][0] = 1; out[2][0][1] = 0; out[2][0][2] = 0;
304 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];
305 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0]; out[4][0][2] = 0;
306 out[5][0][0] = 0; out[5][0][1] = 1; out[5][0][2] = 0;
307 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];
308 out[7][0][0] = 4*in[2]; out[7][0][1] = 0; out[7][0][2] = 4*in[0];
309 out[8][0][0] = 0; out[8][0][1] = 4*in[2]; out[8][0][2] = 4*in[1];
310 out[9][0][0] = 0; out[9][0][1] = 0; out[9][0][2] = 1;
312 out[10][0][0] = 81 * in[1] * in[2] * (1 - 2*in[0] - in[1] - in[2]);
313 out[10][0][1] = 81 * in[0] * in[2] * (1 - in[0] - 2*in[1] - in[2]);
314 out[10][0][2] = 81 * in[0] * in[1] * (1 - in[0] - in[1] - 2*in[2]);
318 void partial (
const std::array<unsigned int, 3>& order,
320 std::vector<typename Traits::RangeType>& out)
const
322 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
323 if (totalOrder == 0) {
324 evaluateFunction(in, out);
325 }
else if (totalOrder == 1) {
327 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
332 out[1] = 4-8*in[0]-4*in[1]-4*in[2];
341 out[10] = 81 * in[1] * in[2] * (1 - 2*in[0] - in[1] - in[2]);
347 out[3] = 4-4*in[0]-8*in[1]-4*in[2];
354 out[10] = 81 * in[0] * in[2] * (1 - in[0] - 2*in[1] - in[2]);
363 out[6] = 4-4*in[0]-4*in[1]-8*in[2];
367 out[10] = 81 * in[0] * in[1] * (1 - in[0] - in[1] - 2*in[2]);
370 DUNE_THROW(RangeError,
"Component out of range.");
373 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
416 static const int numVertices = dim+1;
419 static const int numEdges = (dim+1)*dim / 2;
424 : li(numVertices+numEdges + 1)
427 DUNE_THROW(NotImplemented,
"only for 2d");
441 return numVertices+numEdges + 1;
451 std::vector<Dune::LocalKey> li;
460 template<
typename F,
typename C>
463 typename LB::Traits::DomainType x;
464 typename LB::Traits::RangeType y;
468 auto&& f = Impl::makeFunctionWithCallOperator<decltype(x)>(ff);
471 x[0] = 0.0; x[1] = 0.0; out[0] = f(x);
472 x[0] = 1.0; x[1] = 0.0; out[2] = f(x);
473 x[0] = 0.0; x[1] = 1.0; out[5] = f(x);
476 x[0] = 0.5; x[1] = 0.0; y = f(x);
477 out[1] = y - out[0]*(1-x[0]) - out[2]*x[0];
479 x[0] = 0.0; x[1] = 0.5; y = f(x);
480 out[3] = y - out[0]*(1-x[1]) - out[5]*x[1];
482 x[0] = 0.5; x[1] = 0.5; y = f(x);
483 out[4] = y - out[2]*x[0] - out[5]*x[1];
486 x[0] = 1.0/3; x[1] = 1.0/3; y = f(x);
490 std::vector<typename LB::Traits::RangeType> sfValues;
491 shapeFunctions.evaluateFunction(x, sfValues);
494 for (
int i=0; i<6; i++)
495 out[6] -= out[i]*sfValues[i];
Definition bdfmcube.hh:18
Type traits for LocalBasisVirtualInterface.
Definition common/localbasis.hh:34
D DomainType
domain type
Definition common/localbasis.hh:42
Describe position of one degree of freedom.
Definition localkey.hh:23
Definition hierarchicalsimplexp2withelementbubble.hh:26
HierarchicalSimplexP2WithElementBubbleLocalBasis()
Definition hierarchicalsimplexp2withelementbubble.hh:28
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2withelementbubble.hh:75
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:54
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2withelementbubble.hh:63
unsigned int order() const
Polynomial order of the shape functions (2, in this case)
Definition hierarchicalsimplexp2withelementbubble.hh:111
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2withelementbubble.hh:57
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:86
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:269
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2withelementbubble.hh:275
unsigned int order() const
Polynomial order of the shape functions (4 in this case)
Definition hierarchicalsimplexp2withelementbubble.hh:379
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2withelementbubble.hh:296
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:318
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:266
The local finite element needed for the Zou-Kornhuber estimator for Signorini problems.
Definition hierarchicalsimplexp2withelementbubble.hh:414
size_t size() const
number of coefficients
Definition hierarchicalsimplexp2withelementbubble.hh:439
const Dune::LocalKey & localKey(size_t i) const
get i'th index
Definition hierarchicalsimplexp2withelementbubble.hh:445
HierarchicalSimplexP2WithElementBubbleLocalCoefficients()
Standard constructor.
Definition hierarchicalsimplexp2withelementbubble.hh:423
Definition hierarchicalsimplexp2withelementbubble.hh:456
void interpolate(const F &ff, std::vector< C > &out) const
Local interpolation of a function.
Definition hierarchicalsimplexp2withelementbubble.hh:461