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.");
46 template<
class D,
class R>
62 std::vector<typename Traits::RangeType>& out)
const
67 out[1] = 1-4*(in[0]-0.5)*(in[0]-0.5);
74 std::vector<typename Traits::JacobianType>& out)
const
79 out[1][0][0] = 4-8*in[0];
84 void partial (
const std::array<unsigned int, 1>& order,
86 std::vector<typename Traits::RangeType>& out)
const
88 auto totalOrder = order[0];
89 if (totalOrder == 0) {
90 evaluateFunction(in, out);
91 }
else if (totalOrder == 1) {
96 }
else if (totalOrder == 2) {
103 out[0] = out[1] = out[2] = 0;
136 template<
class D,
class R>
152 std::vector<typename Traits::RangeType>& out)
const
156 out[0] = 1 - in[0] - in[1];
157 out[1] = 4*in[0]*(1-in[0]-in[1]);
159 out[3] = 4*in[1]*(1-in[0]-in[1]);
160 out[4] = 4*in[0]*in[1];
168 std::vector<typename Traits::JacobianType>& out)
const
172 out[0][0][0] = -1; out[0][0][1] = -1;
173 out[1][0][0] = 4-8*in[0]-4*in[1]; out[1][0][1] = -4*in[0];
174 out[2][0][0] = 1; out[2][0][1] = 0;
175 out[3][0][0] = -4*in[1]; out[3][0][1] = 4-4*in[0]-8*in[1];
176 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0];
177 out[5][0][0] = 0; out[5][0][1] = 1;
181 void partial (
const std::array<unsigned int, 2>& order,
183 std::vector<typename Traits::RangeType>& out)
const
185 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
186 if (totalOrder == 0) {
187 evaluateFunction(in, out);
188 }
else if (totalOrder == 1) {
190 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
195 out[1] = 4-8*in[0]-4*in[1];
205 out[3] = 4-4*in[0]-8*in[1];
210 DUNE_THROW(RangeError,
"Component out of range.");
213 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
250 template<
class D,
class R>
266 std::vector<typename Traits::RangeType>& out)
const
270 out[0] = 1 - in[0] - in[1] - in[2];
271 out[1] = 4 * in[0] * (1 - in[0] - in[1] - in[2]);
273 out[3] = 4 * in[1] * (1 - in[0] - in[1] - in[2]);
274 out[4] = 4 * in[0] * in[1];
276 out[6] = 4 * in[2] * (1 - in[0] - in[1] - in[2]);
277 out[7] = 4 * in[0] * in[2];
278 out[8] = 4 * in[1] * in[2];
284 std::vector<typename Traits::JacobianType>& out)
const
288 out[0][0][0] = -1; out[0][0][1] = -1; out[0][0][2] = -1;
289 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];
290 out[2][0][0] = 1; out[2][0][1] = 0; out[2][0][2] = 0;
291 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];
292 out[4][0][0] = 4*in[1]; out[4][0][1] = 4*in[0]; out[4][0][2] = 0;
293 out[5][0][0] = 0; out[5][0][1] = 1; out[5][0][2] = 0;
294 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];
295 out[7][0][0] = 4*in[2]; out[7][0][1] = 0; out[7][0][2] = 4*in[0];
296 out[8][0][0] = 0; out[8][0][1] = 4*in[2]; out[8][0][2] = 4*in[1];
297 out[9][0][0] = 0; out[9][0][1] = 0; out[9][0][2] = 1;
301 void partial (
const std::array<unsigned int, 3>& order,
303 std::vector<typename Traits::RangeType>& out)
const
305 auto totalOrder = std::accumulate(order.begin(), order.end(), 0);
306 if (totalOrder == 0) {
307 evaluateFunction(in, out);
308 }
else if (totalOrder == 1) {
310 auto const direction = std::distance(order.begin(), std::find(order.begin(), order.end(), 1));
315 out[1] = 4-8*in[0]-4*in[1]-4*in[2];
329 out[3] = 4-4*in[0]-8*in[1]-4*in[2];
344 out[6] = 4-4*in[0]-4*in[1]-8*in[2];
350 DUNE_THROW(RangeError,
"Component out of range.");
353 DUNE_THROW(NotImplemented,
"Desired derivative order is not implemented");
Definition bdfmcube.hh:18
Type traits for LocalBasisVirtualInterface.
Definition common/localbasis.hh:35
D DomainType
domain type
Definition common/localbasis.hh:43
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:109
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:52
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:84
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:55
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:73
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:61
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:142
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:181
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:145
unsigned int order() const
Polynomial order of the shape functions (2 in this case)
Definition hierarchicalsimplexp2localbasis.hh:219
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:167
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:151
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:256
void evaluateFunction(const typename Traits::DomainType &in, std::vector< typename Traits::RangeType > &out) const
Evaluate all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:265
void evaluateJacobian(const typename Traits::DomainType &in, std::vector< typename Traits::JacobianType > &out) const
Evaluate Jacobian of all shape functions.
Definition hierarchicalsimplexp2localbasis.hh:283
unsigned int size() const
number of shape functions
Definition hierarchicalsimplexp2localbasis.hh:259
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:301
unsigned int order() const
Polynomial order of the shape functions (2 in this case)
Definition hierarchicalsimplexp2localbasis.hh:359