|
| static std::vector< VectorZd > | HArDCore3D::MonomialPowers< Cell >::homogeneous (const size_t L) |
| |
| static std::vector< VectorZd > | HArDCore3D::MonomialPowers< Cell >::complete (const size_t degree) |
| |
| static std::vector< Eigen::Vector2i > | HArDCore3D::MonomialPowers< Face >::homogeneous (const size_t L) |
| |
| static std::vector< Eigen::Vector2i > | HArDCore3D::MonomialPowers< Face >::complete (size_t degree) |
| |
| | HArDCore3D::MonomialScalarBasisCell::MonomialScalarBasisCell (const Cell &T, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisCell::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::MonomialScalarBasisCell::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| GradientValue | HArDCore3D::MonomialScalarBasisCell::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| HessianValue | HArDCore3D::MonomialScalarBasisCell::hessian (size_t i, const VectorRd &x) const |
| | Evaluate the hessian of the i-th basis function at point x.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisCell::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| VectorZd | HArDCore3D::MonomialScalarBasisCell::powers (size_t i) const |
| | Returns the powers of the i-th basis function (its degree can be found using powers(i).sum())
|
| |
| | HArDCore3D::MonomialScalarBasisFace::MonomialScalarBasisFace (const Face &F, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisFace::dimension () const |
| | Dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::MonomialScalarBasisFace::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
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| GradientValue | HArDCore3D::MonomialScalarBasisFace::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::MonomialScalarBasisFace::curl (size_t i, const VectorRd &x) const |
| | Evaluate the two-dimensional curl of the i-th basis function at point x.
|
| |
| HessianValue | HArDCore3D::MonomialScalarBasisFace::hessian (size_t i, const VectorRd &x) const |
| | Evaluate the Hessian of the i-th basis function at point x.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisFace::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| const VectorRd & | HArDCore3D::MonomialScalarBasisFace::normal () const |
| | Return the normal to the face used in the computation of the curl.
|
| |
| const JacobianType & | HArDCore3D::MonomialScalarBasisFace::jacobian () const |
| | Return the Jacobian of the coordinate system transformation.
|
| |
| const JacobianType | HArDCore3D::MonomialScalarBasisFace::coordinates_system () const |
| | Return the system of coordinates (basis in rows) on the face.
|
| |
| Eigen::Vector2i | HArDCore3D::MonomialScalarBasisFace::powers (size_t i) const |
| | Returns the powers of the i-th basis function (its degree can be found using powers(i).sum())
|
| |
| | HArDCore3D::MonomialScalarBasisEdge::MonomialScalarBasisEdge (const Edge &E, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisEdge::dimension () const |
| | Dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::MonomialScalarBasisEdge::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
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| GradientValue | HArDCore3D::MonomialScalarBasisEdge::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| size_t | HArDCore3D::MonomialScalarBasisEdge::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| | HArDCore3D::Family< BasisType >::Family (const BasisType &basis, const Eigen::MatrixXd &matrix) |
| | Constructor.
|
| |
| size_t | HArDCore3D::Family< BasisType >::dimension () const |
| | Dimension of the family. This is actually the number of functions in the family, not necessarily linearly independent.
|
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| FunctionValue | HArDCore3D::Family< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th function at point x.
|
| |
| FunctionValue | HArDCore3D::Family< BasisType >::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)
|
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| GradientValue | HArDCore3D::Family< BasisType >::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th function at point x.
|
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| GradientValue | HArDCore3D::Family< BasisType >::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)
|
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| CurlValue | HArDCore3D::Family< BasisType >::curl (size_t i, const VectorRd &x) const |
| | Evaluate the curl of the i-th function at point x.
|
| |
| CurlValue | HArDCore3D::Family< BasisType >::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)
|
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| DivergenceValue | HArDCore3D::Family< BasisType >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th function at point x.
|
| |
| DivergenceValue | HArDCore3D::Family< BasisType >::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)
|
| |
| HessianValue | HArDCore3D::Family< BasisType >::hessian (size_t i, const VectorRd &x) const |
| | Evaluate the hessian of the i-th function at point x.
|
| |
| HessianValue | HArDCore3D::Family< BasisType >::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 & | HArDCore3D::Family< BasisType >::matrix () const |
| | Return the coefficient matrix.
|
| |
| constexpr const BasisType & | HArDCore3D::Family< BasisType >::ancestor () const |
| | Return the ancestor.
|
| |
| size_t | HArDCore3D::Family< BasisType >::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::TensorizedVectorFamily (const ScalarFamilyType &scalar_family) |
| |
| size_t | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::dimension () const |
| | Return the dimension of the family.
|
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| FunctionValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
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| FunctionValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::function (size_t i, size_t iqn, const boost::multi_array< double, 2 > &ancestor_value_quad) const |
| | Evaluate the i-th basis function at a quadrature point iqn, knowing all the values of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
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| GradientValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| GradientValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::gradient (size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_gradient_quad) const |
| | Evaluate the gradient of the i-th basis function at a quadrature point iqn, knowing all the gradients of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| CurlValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::curl (size_t i, const VectorRd &x) const |
| | Evaluate the curl of the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::curl (size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_gradient_quad) const |
| | Evaluate the curl of the i-th basis function at a quadrature point iqn, knowing all the gradients of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| DivergenceValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::divergence (size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_gradient_quad) const |
| | Evaluate the divergence of the i-th basis function at a quadrature point iqn, knowing all the gradients of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| CurlValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::curlcurl (size_t i, const VectorRd &x) const |
| | Evaluate the curl curl of the i-th basis function at point x. We use the formula curl curl = - Laplace + grad div.
|
| |
| CurlValue | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::curlcurl (size_t i, size_t iqn, const boost::multi_array< typename ScalarFamilyType::HessianValue, 2 > &ancestor_hessian_quad) const |
| | Evaluate the curl curl of the i-th basis function at a quadrature point iqn, knowing all the values of the Hessian of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| constexpr const ScalarFamilyType & | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::ancestor () const |
| | Return the ancestor (family that has been tensorized)
|
| |
| size_t | HArDCore3D::TensorizedVectorFamily< ScalarFamilyType, N >::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::MatrixFamily (const ScalarFamilyType &scalar_family) |
| |
| size_t | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::dimension () const |
| | Return the dimension of the family.
|
| |
| FunctionValue | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| FunctionValue | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::function (size_t i, size_t iqn, const boost::multi_array< double, 2 > &ancestor_value_quad) const |
| | Evaluate the i-th basis function at a quadrature point iqn, knowing all the values of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| DivergenceValue | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::divergence (size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_gradient_quad) const |
| | Evaluate the divergence of the i-th basis function at a quadrature point iqn, knowing all the gradients of ancestor basis functions at the quadrature nodes (provided by eval_quad)
|
| |
| const ScalarFamilyType & | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::ancestor () const |
| | Return the ancestor (family that has been tensorized)
|
| |
| const size_t | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::matrixSize () const |
| | Return the dimension of the matrices in the family.
|
| |
| const Eigen::MatrixXd | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::transposeOperator () const |
| | Return the transpose operator, the rN^2 square matrix that to a given vector of coefficients on the Matrix family associates the vector of coefficients corresponding to the transpose.
|
| |
| const Eigen::MatrixXd | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::symmetriseOperator () const |
| | Return the symmetrisation operator, the rN^2 square matrix that to a given vector of coefficients on the Matrix family associates the vector of coefficients corresponding to the symmetrised matrix.
|
| |
| const Eigen::MatrixXd | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::symmetricBasis () const |
| | Returns the matrix that can be used, in a Family of this MatrixBasis, to create a basis of the subspace of symmetric matrices.
|
| |
| const Eigen::MatrixXd | HArDCore3D::MatrixFamily< ScalarFamilyType, N >::traceOperator () const |
| | Returns the matrix corresponding to the trace, expressed as a linear operator between that MatrixFamily and the underlying scalar family.
|
| |
| | HArDCore3D::TangentFamily< ScalarFamilyType >::TangentFamily (const ScalarFamilyType &scalar_family, const Eigen::Matrix< double, 2, dimspace > &generators) |
| | Constructor.
|
| |
| size_t | HArDCore3D::TangentFamily< ScalarFamilyType >::dimension () const |
| | Return the dimension of the family.
|
| |
| FunctionValue | HArDCore3D::TangentFamily< ScalarFamilyType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::TangentFamily< ScalarFamilyType >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::TangentFamily< ScalarFamilyType >::curlcurl (size_t i, const VectorRd &x) const |
| | Evaluate the curl curl of the i-th basis function at point x.
|
| |
| constexpr const ScalarFamilyType & | HArDCore3D::TangentFamily< ScalarFamilyType >::ancestor () const |
| | Return the ancestor (family used for the tangent)
|
| |
| size_t | HArDCore3D::TangentFamily< ScalarFamilyType >::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| Eigen::Matrix< double, 2, dimspace > | HArDCore3D::TangentFamily< ScalarFamilyType >::generators () const |
| | Returns the generators of the basis functions.
|
| |
| | HArDCore3D::ShiftedBasis< BasisType >::ShiftedBasis (const BasisType &basis, const int shift) |
| | Constructor.
|
| |
| size_t | HArDCore3D::ShiftedBasis< BasisType >::dimension () const |
| | Return the dimension of the basis.
|
| |
| size_t | HArDCore3D::ShiftedBasis< BasisType >::shift () const |
| | Return the shift.
|
| |
| constexpr const BasisType & | HArDCore3D::ShiftedBasis< BasisType >::ancestor () const |
| | Return the underlying complete basis.
|
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| size_t | HArDCore3D::ShiftedBasis< BasisType >::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
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| FunctionValue | HArDCore3D::ShiftedBasis< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
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| GradientValue | HArDCore3D::ShiftedBasis< BasisType >::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::ShiftedBasis< BasisType >::curl (size_t i, const VectorRd &x) const |
| | Evaluate the curl of the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::ShiftedBasis< BasisType >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| HessianValue | HArDCore3D::ShiftedBasis< BasisType >::hessian (size_t i, const VectorRd &x) const |
| | Evaluate the hessian of the i-th basis function at point x.
|
| |
| | HArDCore3D::RestrictedBasis< BasisType >::RestrictedBasis (const BasisType &basis, const size_t &dimension) |
| | Constructor.
|
| |
| size_t | HArDCore3D::RestrictedBasis< BasisType >::dimension () const |
| | Return the dimension of the basis.
|
| |
| constexpr const BasisType & | HArDCore3D::RestrictedBasis< BasisType >::ancestor () const |
| | Return the underlying complete basis.
|
| |
| size_t | HArDCore3D::RestrictedBasis< BasisType >::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| FunctionValue | HArDCore3D::RestrictedBasis< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
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| GradientValue | HArDCore3D::RestrictedBasis< BasisType >::gradient (size_t i, const VectorRd &x) const |
| | Evaluate the gradient of the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::RestrictedBasis< BasisType >::curl (size_t i, const VectorRd &x) const |
| | Evaluate the curl of the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::RestrictedBasis< BasisType >::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| HessianValue | HArDCore3D::RestrictedBasis< BasisType >::hessian (size_t i, const VectorRd &x) const |
| | Evaluate the hessian of the i-th basis function at point x.
|
| |
| | HArDCore3D::GradientBasis< BasisType >::GradientBasis (const BasisType &basis) |
| | Constructor.
|
| |
| size_t | HArDCore3D::GradientBasis< BasisType >::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::GradientBasis< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| constexpr const BasisType & | HArDCore3D::GradientBasis< BasisType >::ancestor () const |
| | Return the ancestor (basis that the gradient was taken of)
|
| |
| | HArDCore3D::CurlBasis< BasisType >::CurlBasis (const BasisType &basis) |
| | Constructor.
|
| |
| size_t | HArDCore3D::CurlBasis< BasisType >::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::CurlBasis< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| constexpr const BasisType & | HArDCore3D::CurlBasis< BasisType >::ancestor () const |
| | Return the ancestor (basis that the gradient was taken of)
|
| |
| | HArDCore3D::DivergenceBasis< BasisType >::DivergenceBasis (const BasisType &basis) |
| | Constructor.
|
| |
| size_t | HArDCore3D::DivergenceBasis< BasisType >::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::DivergenceBasis< BasisType >::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| constexpr const BasisType & | HArDCore3D::DivergenceBasis< BasisType >::ancestor () const |
| | Return the ancestor (basis that the gradient was taken of)
|
| |
| template<typename ScalarFamilyType > |
| DivergenceBasis< TangentFamily< ScalarFamilyType > > | HArDCore3D::ScalarRotFamily (const TangentFamily< ScalarFamilyType > &tangent_family, const Face &F) |
| | The following function creates the "scalar rot" basis of a TangentFamily on a face.
|
| |
| | HArDCore3D::RolyComplBasisCell::RolyComplBasisCell (const Cell &T, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::RolyComplBasisCell::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::RolyComplBasisCell::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::RolyComplBasisCell::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| size_t | HArDCore3D::RolyComplBasisCell::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| VectorZd | HArDCore3D::RolyComplBasisCell::powers (size_t i) const |
| | Returns the powers of the i-th basis function (not including the vector part)
|
| |
| | HArDCore3D::GolyComplBasisCell::GolyComplBasisCell (const Cell &T, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::GolyComplBasisCell::dimension () const |
| | Compute the dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::GolyComplBasisCell::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| CurlValue | HArDCore3D::GolyComplBasisCell::curl (size_t i, const VectorRd &x) const |
| | Evaluate the curl of the i-th basis function at point x.
|
| |
| size_t | HArDCore3D::GolyComplBasisCell::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| VectorZd | HArDCore3D::GolyComplBasisCell::powers (size_t i) const |
| | Returns the powers of the i-th basis function (not including the vector part)
|
| |
| size_t | HArDCore3D::GolyComplBasisCell::dimPkmo () const |
| | Returns the dimension of P^{k-1}(R^3)
|
| |
| | HArDCore3D::RolyComplBasisFace::RolyComplBasisFace (const Face &F, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::RolyComplBasisFace::dimension () const |
| | Dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::RolyComplBasisFace::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| DivergenceValue | HArDCore3D::RolyComplBasisFace::divergence (size_t i, const VectorRd &x) const |
| | Evaluate the divergence of the i-th basis function at point x.
|
| |
| const JacobianType & | HArDCore3D::RolyComplBasisFace::jacobian () const |
| | Return the Jacobian of the coordinate system transformation.
|
| |
| size_t | HArDCore3D::RolyComplBasisFace::max_degree () const |
| | Returns the maximum degree of the basis functions.
|
| |
| Eigen::Vector2i | HArDCore3D::RolyComplBasisFace::powers (size_t i) const |
| | Returns the powers of the i-th basis function.
|
| |
| | HArDCore3D::GolyComplBasisFace::GolyComplBasisFace (const Face &F, size_t degree) |
| | Constructor.
|
| |
| size_t | HArDCore3D::GolyComplBasisFace::dimension () const |
| | Dimension of the basis.
|
| |
| FunctionValue | HArDCore3D::GolyComplBasisFace::function (size_t i, const VectorRd &x) const |
| | Evaluate the i-th basis function at point x.
|
| |
| const VectorRd & | HArDCore3D::GolyComplBasisFace::normal () const |
| | Return the normal to the face used in the computation of the curl.
|
| |
| const std::shared_ptr< RolyComplBasisFace > & | HArDCore3D::GolyComplBasisFace::rck () const |
| | Return the Rck basis.
|
| |
| template<typename outValue , typename inValue , typename FunctionType > |
| boost::multi_array< outValue, 2 > | HArDCore3D::transform_values_quad (const boost::multi_array< inValue, 2 > &B_quad, const FunctionType &F) |
| | Takes an array B_quad of values at quadrature nodes and applies the function F to all of them. F must take inValue and return outValue. The function must be called with outValue as template argument: transform_values_quad<outValue>(...)
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| template<typename ScalarBasisType , size_t N> |
| Family< TensorizedVectorFamily< ScalarBasisType, N > > | HArDCore3D::GenericTensorization (const ScalarBasisType &B, const std::vector< Eigen::VectorXd > &v) |
| | From a scalar family B=(B_1..B_r) and vectors (v_1..v_k) in R^N, constructs a "Family" of "TensorizedVectorFamily" (built on B, of size N) that represents the family (B_1v_1..B_rv_1 B_1v_2...B_rv_2...B_1v_k...B_rv_k).
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| Eigen::MatrixXd | HArDCore3D::PermuteTensorization (const size_t a, const size_t b) |
| | Returns the matrix giving the permutation of the tensorization of a family of size a with a family of size b.
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| template<typename ScalarBasisType , size_t N> |
| Family< MatrixFamily< ScalarBasisType, N > > | HArDCore3D::IsotropicMatrixFamily (const ScalarBasisType &B) |
| | From a scalar family B, constructs a "Family" of "MatrixFamily" (built on B, of size NxN) that represents the family B Id on the MatrixFamily.
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Function >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Function >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_value_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Gradient >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Gradient >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_gradient_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Curl >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Curl >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_curl_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Divergence >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Divergence >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_divergence_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Hessian >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, Hessian >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_hessian_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, CurlCurl >::evaluate (const BasisType &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< BasisType, CurlCurl >::evaluate (const BasisType &basis, size_t i, size_t iqn, const boost::multi_array< ReturnValue, 2 > &ancestor_curlcurl_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Function >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Function >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< double, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Gradient >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Gradient >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Curl >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Curl >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Divergence >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, Divergence >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, CurlCurl >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< TensorizedVectorFamily< ScalarBasisType, N >, CurlCurl >::evaluate (const TensorizedVectorFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< MatrixRd, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< MatrixFamily< ScalarBasisType, N >, Function >::evaluate (const MatrixFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< MatrixFamily< ScalarBasisType, N >, Function >::evaluate (const MatrixFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< double, 2 > &ancestor_basis_quad) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< MatrixFamily< ScalarBasisType, N >, Divergence >::evaluate (const MatrixFamily< ScalarBasisType, N > &basis, size_t i, const VectorRd &x) |
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| static ReturnValue | HArDCore3D::detail::basis_evaluation_traits< MatrixFamily< ScalarBasisType, N >, Divergence >::evaluate (const MatrixFamily< ScalarBasisType, N > &basis, size_t i, size_t iqn, const boost::multi_array< VectorRd, 2 > &ancestor_basis_quad) |
| |
| template<typename BasisType > |
| static boost::multi_array< typename detail::basis_evaluation_traits< BasisType, BasisFunction >::ReturnValue, 2 > | HArDCore3D::evaluate_quad< BasisFunction >::compute (const BasisType &basis, const QuadratureRule &quad) |
| | Generic basis evaluation.
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| |
| template<typename BasisType > |
| static boost::multi_array< typename detail::basis_evaluation_traits< Family< BasisType >, BasisFunction >::ReturnValue, 2 > | HArDCore3D::evaluate_quad< BasisFunction >::compute (const Family< BasisType > &basis, const QuadratureRule &quad) |
| | Evaluate a 'Family' of functions at quadrature nodes (optimised compared the generic basis evaluation, to avoid computing several times the ancestor basis at the quadrature nodes)
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| template<typename BasisType , size_t N> |
| static boost::multi_array< typename detail::basis_evaluation_traits< TensorizedVectorFamily< BasisType, N >, BasisFunction >::ReturnValue, 2 > | HArDCore3D::evaluate_quad< BasisFunction >::compute (const TensorizedVectorFamily< BasisType, N > &basis, const QuadratureRule &quad) |
| | Evaluate a tensorized family at quadrature nodes (optimised compared the generic basis evaluation, to avoid computing several times the ancestor basis at the quadrature nodes)
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| template<typename BasisType , size_t N> |
| static boost::multi_array< typename detail::basis_evaluation_traits< MatrixFamily< BasisType, N >, BasisFunction >::ReturnValue, 2 > | HArDCore3D::evaluate_quad< BasisFunction >::compute (const MatrixFamily< BasisType, N > &basis, const QuadratureRule &quad) |
| | Evaluate a Matrix family at quadrature nodes (optimised compared the generic basis evaluation, to avoid computing several times the ancestor basis at the quadrature nodes)
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| |
| template<typename T > |
| Eigen::MatrixXd | HArDCore3D::gram_schmidt (boost::multi_array< T, 2 > &basis_eval, const std::function< double(size_t, size_t)> &inner_product) |
| |
| double | HArDCore3D::scalar_product (const double &x, const double &y) |
| | Scalar product between two reals.
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| double | HArDCore3D::scalar_product (const double &x, const Eigen::Matrix< double, 1, 1 > &y) |
| | Scalar product between one real and one 1-dimension Eigen vector.
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| double | HArDCore3D::scalar_product (const VectorRd &x, const VectorRd &y) |
| | Scalar product between two vectors.
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| template<int N> |
| double | HArDCore3D::scalar_product (const Eigen::Matrix< double, N, N > &x, const Eigen::Matrix< double, N, N > &y) |
| | Scalar product between two matrices.
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| |
| template<typename Value > |
| boost::multi_array< double, 2 > | HArDCore3D::scalar_product (const boost::multi_array< Value, 2 > &basis_quad, const Value &v) |
| | This overloading of the scalar_product function computes the scalar product between an evaluation of a basis and a constant value; both basis values and constant value must be of type Value.
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| boost::multi_array< VectorRd, 2 > | HArDCore3D::vector_product (const boost::multi_array< VectorRd, 2 > &basis_quad, const VectorRd &v) |
| | Compute the vector (cross) product between the evaluation of a basis and a constant vector.
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| |
| template<typename BasisType > |
| Family< BasisType > | HArDCore3D::l2_orthonormalize (const BasisType &basis, const QuadratureRule &qr, boost::multi_array< typename BasisType::FunctionValue, 2 > &basis_quad) |
| | \(L^2\)-orthonormalization: simply consists in using gram_schmidt() with the specific l2 inner product
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| |
| template<typename BasisType > |
| Family< BasisType > | HArDCore3D::l2_orthonormalize (const BasisType &basis, const Eigen::MatrixXd &GM) |
| | \(L^2\)-orthonormalization: when the Gram Matrix is passed, we use Cholesky.
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| |
| template<typename FunctionValue > |
| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< FunctionValue, 2 > &B1, const boost::multi_array< FunctionValue, 2 > &B2, const QuadratureRule &qr, const size_t nrows, const size_t ncols, const std::string sym="nonsym") |
| |
| template<typename FunctionValue > |
| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< FunctionValue, 2 > &B1, const boost::multi_array< FunctionValue, 2 > &B2, const QuadratureRule &qr, const std::string sym="nonsym") |
| |
| template<typename FunctionValue > |
| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< FunctionValue, 2 > &B, const QuadratureRule &qr) |
| | Compute the Gram matrix given the evaluation of one family of functions at quadrature nodes. Consists in calling the generic templated version with B1=B2.
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| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< VectorRd, 2 > &B1, const boost::multi_array< double, 2 > &B2, const QuadratureRule &qr) |
| | Compute the Gram-like matrix given a family of vector-valued and one of scalar-valued functions by tensorizing the latter.
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| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< double, 2 > &B1, const boost::multi_array< double, 2 > &B2, const QuadratureRule &qr, const size_t nrows, const size_t ncols, const std::string sym) |
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| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< double, 2 > &B1, const boost::multi_array< double, 2 > &B2, const QuadratureRule &qr, const std::string sym) |
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| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< VectorRd, 2 > &B1, const boost::multi_array< VectorRd, 2 > &B2, const QuadratureRule &qr, const size_t nrows, const size_t ncols, const std::string sym) |
| |
| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const boost::multi_array< VectorRd, 2 > &B1, const boost::multi_array< VectorRd, 2 > &B2, const QuadratureRule &qr, const std::string sym="nonsym") |
| | Compute the Gram-like matrix given the evaluation of two families of functions at quadrature nodes. Consists in calling the Vector3d-valued version with nrows = nb of elements in B1, ncols = nb of elements in B2.
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| template<typename ScalarFamilyType , size_t N> |
| Eigen::MatrixXd | HArDCore3D::compute_gram_matrix (const MatrixFamily< ScalarFamilyType, N > &MatFam, const boost::multi_array< double, 2 > &scalar_family_quad, const QuadratureRule &qr) |
| | Compute the Gram-like matrix for a MatrixFamily. This overload is more efficient than the generic function as it only computes the gram matrix of the underlying scalar family, and then creates the bloc-diagonal gram matrix of the MatrixFamily (which is indeed bloc diagonal given the choice of m_E elements in this class).
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| |
| template<typename T > |
| Eigen::VectorXd | HArDCore3D::integrate (const FType< T > &f, const BasisQuad< T > &B, const QuadratureRule &qr, size_t n_rows=0) |
| | Computes the vector of integrals (f, phi_i)
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| |
| template<typename T , typename U > |
| Eigen::MatrixXd | HArDCore3D::compute_weighted_gram_matrix (const FType< U > &f, const BasisQuad< T > &B1, const BasisQuad< T > &B2, const QuadratureRule &qr, size_t n_rows=0, size_t n_cols=0, const std::string sym="nonsym") |
| | Computes the Gram-like matrix of integrals (f phi_i, phi_j)
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| |
| template<typename T , typename U > |
| Eigen::MatrixXd | HArDCore3D::compute_weighted_gram_matrix (const FType< U > &f, const BasisQuad< T > &B1, const BasisQuad< T > &B2, const QuadratureRule &qr, const std::string sym) |
| | Computes the Gram-like matrix of integrals (f phi_i, phi_j)
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| Eigen::MatrixXd | HArDCore3D::compute_weighted_gram_matrix (const FType< VectorRd > &f, const BasisQuad< VectorRd > &B1, const BasisQuad< double > &B2, const QuadratureRule &qr, size_t n_rows=0, size_t n_cols=0) |
| | Computes the Gram-like matrix of integrals (f dot phi_i, phi_j)
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| |
| Eigen::MatrixXd | HArDCore3D::compute_weighted_gram_matrix (const FType< VectorRd > &f, const BasisQuad< double > &B1, const BasisQuad< VectorRd > &B2, const QuadratureRule &qr, size_t n_rows=0, size_t n_cols=0) |
| | Computes the Gram-like matrix of integrals (phi_i, f dot phi_j)
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| template<typename BasisType > |
| Eigen::VectorXd | HArDCore3D::l2_projection (const std::function< typename BasisType::FunctionValue(const VectorRd &)> &f, const BasisType &basis, QuadratureRule &quad, const boost::multi_array< typename BasisType::FunctionValue, 2 > &basis_quad, const Eigen::MatrixXd &mass_basis=Eigen::MatrixXd::Zero(1, 1)) |
| | Compute the L2-projection of a function.
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| | HArDCore3D::DecomposePoly< BasisType >::DecomposePoly (const Face &F, const BasisType &basis) |
| | Constructor for face.
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| | HArDCore3D::DecomposePoly< BasisType >::DecomposePoly (const Cell &T, const BasisType &basis) |
| | Constructor for cell.
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| QuadratureRule | HArDCore3D::DecomposePoly< BasisType >::get_nodes () const |
| | Return the set of nodes (useful to compute value of polynomial to decompose via evaluate_quad)
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| Family< BasisType > | HArDCore3D::DecomposePoly< BasisType >::family (boost::multi_array< typename BasisType::FunctionValue, 2 > &values) |
| | Returns the decomposed polynomials as a Family of the provided basis.
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| |
Classes and functions for polynomial basis creation and manipulation.
