5#ifndef DUNE_HIERARCHICAL_SIMPLEX_P2_LOCALBASIS_HH
6#define DUNE_HIERARCHICAL_SIMPLEX_P2_LOCALBASIS_HH
14#include <dune/common/fvector.hh>
15#include <dune/common/fmatrix.hh>
21 template<
class D,
class R,
int dim>
27 DUNE_THROW(Dune::NotImplemented,
"HierarchicalSimplexP2LocalBasis not implemented for dim > 3.");
45 template<
class D,
class R>
61 std::vector<typename Traits::RangeType>& out)
const
66 out[1] = 1-4*(in[0]-0.5)*(in[0]-0.5);
73 std::vector<typename Traits::JacobianType>& out)
const
78 out[1][0][0] = 4-8*in[0];
83 void partial (
const std::array<unsigned int, 1>& order,
85 std::vector<typename Traits::RangeType>& out)
const
87 auto totalOrder = order[0];
88 if (totalOrder == 0) {
89 evaluateFunction(in, out);
90 }
else if (totalOrder == 1) {
95 }
else if (totalOrder == 2) {
102 out[0] = out[1] = out[2] = 0;
134 template<
class D,
class R>
150 std::vector<typename Traits::RangeType>& out)
const
154 out[0] = 1 - in[0] - in[1];
155 out[1] = 4*in[0]*(1-in[0]-in[1]);
157 out[3] = 4*in[1]*(1-in[0]-in[1]);
158 out[4] = 4*in[0]*in[1];
166 std::vector<typename Traits::JacobianType>& out)
const
170 out[0][0][0] = -1; out[0][0][1] = -1;
171 out[1][0][0] = 4-8*in[0]-4*in[1]; out[1][0][1] = -4*in[0];
172 out[2][0][0] = 1; out[2][0][1] = 0;
173 out[3][0][0] = -4*in[1]; out[3][0][1] = 4-4*in[0]-8*in[1];
174 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0];
175 out[5][0][0] = 0; out[5][0][1] = 1;
179 void partial (
const std::array<unsigned int, 2>& order,
181 std::vector<typename Traits::RangeType>& out)
const
183 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
184 if (totalOrder == 0) {
185 evaluateFunction(in, out);
186 }
else if (totalOrder == 1) {
188 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
193 out[1] = 4-8*in[0]-4*in[1];
203 out[3] = 4-4*in[0]-8*in[1];
208 DUNE_THROW(RangeError,
"Component out of range.");
211 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
247 template<
class D,
class R>
263 std::vector<typename Traits::RangeType>& out)
const
267 out[0] = 1 - in[0] - in[1] - in[2];
268 out[1] = 4 * in[0] * (1 - in[0] - in[1] - in[2]);
270 out[3] = 4 * in[1] * (1 - in[0] - in[1] - in[2]);
271 out[4] = 4 * in[0] * in[1];
273 out[6] = 4 * in[2] * (1 - in[0] - in[1] - in[2]);
274 out[7] = 4 * in[0] * in[2];
275 out[8] = 4 * in[1] * in[2];
281 std::vector<typename Traits::JacobianType>& out)
const
285 out[0][0][0] = -1; out[0][0][1] = -1; out[0][0][2] = -1;
286 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];
287 out[2][0][0] = 1; out[2][0][1] = 0; out[2][0][2] = 0;
288 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];
289 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0]; out[4][0][2] = 0;
290 out[5][0][0] = 0; out[5][0][1] = 1; out[5][0][2] = 0;
291 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];
292 out[7][0][0] = 4*in[2]; out[7][0][1] = 0; out[7][0][2] = 4*in[0];
293 out[8][0][0] = 0; out[8][0][1] = 4*in[2]; out[8][0][2] = 4*in[1];
294 out[9][0][0] = 0; out[9][0][1] = 0; out[9][0][2] = 1;
298 void partial (
const std::array<unsigned int, 3>& order,
300 std::vector<typename Traits::RangeType>& out)
const
302 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
303 if (totalOrder == 0) {
304 evaluateFunction(in, out);
305 }
else if (totalOrder == 1) {
307 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
312 out[1] = 4-8*in[0]-4*in[1]-4*in[2];
326 out[3] = 4-4*in[0]-8*in[1]-4*in[2];
341 out[6] = 4-4*in[0]-4*in[1]-8*in[2];
347 DUNE_THROW(RangeError,
"Component out of range.");
350 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
Definition bdfmcube.hh:18
Type traits for LocalBasisVirtualInterface.
Definition common/localbasis.hh:34
D DomainType
domain type
Definition common/localbasis.hh:42
Definition hierarchicalsimplexp2localbasis.hh:23
HierarchicalSimplexP2LocalBasis()
Definition hierarchicalsimplexp2localbasis.hh:25
unsigned int order() const
Polynomial order of the shape functions (2, in this case)
Definition hierarchicalsimplexp2localbasis.hh:108
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 hierarchicalsimplexp2localbasis.hh:51
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 hierarchicalsimplexp2localbasis.hh:83
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:54
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:72
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:60
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 hierarchicalsimplexp2localbasis.hh:140
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 hierarchicalsimplexp2localbasis.hh:179
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:143
unsigned int order() const
Polynomial order of the shape functions (2 in this case)
Definition hierarchicalsimplexp2localbasis.hh:217
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:165
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:149
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 hierarchicalsimplexp2localbasis.hh:253
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:262
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:280
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:256
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 hierarchicalsimplexp2localbasis.hh:298
unsigned int order() const
Polynomial order of the shape functions (2 in this case)
Definition hierarchicalsimplexp2localbasis.hh:356