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HArD::Core2D
Hybrid Arbitrary Degree::Core 2D - Library to implement 2D schemes with edge and cell polynomials as unknowns
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#include <basis.hpp>
Public Types | |
| typedef BasisType::FunctionValue | FunctionValue |
| typedef BasisType::GradientValue | GradientValue |
| typedef BasisType::CurlValue | CurlValue |
| typedef BasisType::DivergenceValue | DivergenceValue |
| typedef BasisType::RotorValue | RotorValue |
| typedef BasisType::HessianValue | HessianValue |
| typedef BasisType::GeometricSupport | GeometricSupport |
| typedef BasisType | AncestorType |
Public Member Functions | |
| Family (const BasisType &basis, const Eigen::MatrixXd &matrix) | |
| Constructor. | |
| size_t | dimension () const |
| Dimension of the family. This is actually the number of functions in the family, not necessarily linearly independent. | |
| FunctionValue | function (size_t i, const VectorRd &x) const |
| Evaluate the i-th function at point x. | |
| FunctionValue | function (size_t i, size_t iqn, const boost::multi_array< FunctionValue, 2 > &ancestor_value_quad) const |
| Evaluate the i-th function at a quadrature point iqn, knowing all the values of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| GradientValue | gradient (size_t i, const VectorRd &x) const |
| Evaluate the gradient of the i-th function at point x. | |
| GradientValue | gradient (size_t i, size_t iqn, const boost::multi_array< GradientValue, 2 > &ancestor_gradient_quad) const |
| Evaluate the gradient of the i-th function at a quadrature point iqn, knowing all the gradients of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| CurlValue | curl (size_t i, const VectorRd &x) const |
| Evaluate the curl of the i-th function at point x. | |
| CurlValue | curl (size_t i, size_t iqn, const boost::multi_array< CurlValue, 2 > &ancestor_curl_quad) const |
| Evaluate the curl of the i-th function at a quadrature point iqn, knowing all the curls of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| DivergenceValue | divergence (size_t i, const VectorRd &x) const |
| Evaluate the divergence of the i-th function at point x. | |
| DivergenceValue | divergence (size_t i, size_t iqn, const boost::multi_array< DivergenceValue, 2 > &ancestor_divergence_quad) const |
| Evaluate the divergence of the i-th function at a quadrature point iqn, knowing all the divergences of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| DivergenceValue | rotor (size_t i, const VectorRd &x) const |
| Evaluate the scalar rotor of the i-th function at point x. | |
| RotorValue | rotor (size_t i, size_t iqn, const boost::multi_array< RotorValue, 2 > &ancestor_rotor_quad) const |
| Evaluate the scalar rotor of the i-th function at a quadrature point iqn, knowing all the scalar rotors of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| HessianValue | hessian (size_t i, const VectorRd &x) const |
| Evaluate the Hessian of the i-th basis function at point x. | |
| HessianValue | hessian (size_t i, size_t iqn, const boost::multi_array< HessianValue, 2 > &ancestor_hessian_quad) const |
| Evaluate the hessian of the i-th function at a quadrature point iqn, knowing all the hessian of ancestor basis functions at the quadrature nodes (provided by eval_quad) | |
| const Eigen::MatrixXd & | matrix () const |
| Return the coefficient matrix. | |
| constexpr const BasisType & | ancestor () const |
| Return the ancestor. | |
| size_t | max_degree () const |
| Returns the maximum degree of the basis functions. | |
Static Public Attributes | |
| static constexpr const TensorRankE | tensorRank = BasisType::tensorRank |
| static constexpr const bool | hasAncestor = true |
| static const bool | hasFunction = BasisType::hasFunction |
| static const bool | hasGradient = BasisType::hasGradient |
| static const bool | hasCurl = BasisType::hasCurl |
| static const bool | hasDivergence = BasisType::hasDivergence |
| static const bool | hasRotor = BasisType::hasRotor |
| static const bool | hasHessian = BasisType::hasHessian |
Family of functions expressed as linear combination of the functions of a given basis
If \((f_1,...,f_r)\) is the basis, then the family is \((\phi_1,...,\phi_l)\) where \(\phi_i = \sum_j M_ij f_j\). The matrix \(M\) is the member m_matrix.
1.9.8