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HArD::Core3D
Hybrid Arbitrary Degree::Core 3D - Library to implement 3D schemes with vertex, edge, face and cell polynomials as unknowns
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Vector family obtained by tensorization of a scalar family. More...
#include <basis.hpp>
Public Types | |
| typedef Eigen::Matrix< double, N, 1 > | FunctionValue |
| typedef Eigen::Matrix< double, N, dimspace > | GradientValue |
| typedef VectorRd | CurlValue |
| typedef double | DivergenceValue |
| typedef void | HessianValue |
| typedef ScalarFamilyType::GeometricSupport | GeometricSupport |
| typedef ScalarFamilyType | AncestorType |
Public Member Functions | |
| TensorizedVectorFamily (const ScalarFamilyType &scalar_family) | |
| size_t | dimension () const |
| Return the dimension of the family. More... | |
| FunctionValue | function (size_t i, const VectorRd &x) const |
| Evaluate the i-th basis function at point x. More... | |
| FunctionValue | 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) More... | |
| GradientValue | gradient (size_t i, const VectorRd &x) const |
| Evaluate the gradient of the i-th basis function at point x. More... | |
| GradientValue | 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) More... | |
| CurlValue | curl (size_t i, const VectorRd &x) const |
| Evaluate the curl of the i-th basis function at point x. More... | |
| CurlValue | 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) More... | |
| DivergenceValue | divergence (size_t i, const VectorRd &x) const |
| Evaluate the divergence of the i-th basis function at point x. More... | |
| DivergenceValue | 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) More... | |
| CurlValue | 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. More... | |
| CurlValue | 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) More... | |
| constexpr const ScalarFamilyType & | ancestor () const |
| Return the ancestor (family that has been tensorized) More... | |
| size_t | max_degree () const |
| Returns the maximum degree of the basis functions. More... | |
Static Public Attributes | |
| constexpr static const TensorRankE | tensorRank = Vector |
| constexpr static const bool | hasAncestor = true |
| static const bool | hasFunction = ScalarFamilyType::hasFunction |
| static const bool | hasGradient = ScalarFamilyType::hasGradient |
| static const bool | hasDivergence = (ScalarFamilyType::hasGradient && N == dimspace) |
| static const bool | hasCurl = (ScalarFamilyType::hasGradient && N == dimspace) |
| static const bool | hasHessian = false |
| static const bool | hasCurlCurl = (ScalarFamilyType::hasHessian && N == dimspace) |
Vector family obtained by tensorization of a scalar family.
The tensorization is done the following way: if \((f_1,...,f_r)\) is the family of scalar functions, the tensorized family of rank N is given by (where all vectors are columns of size N):
\(\left(\begin{array}{c}f_1\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}f_2\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}f_r\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}0\\f_1\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}0\\f_2\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}0\\f_r\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}0\\\vdots\\0\\f_1\end{array}\right)\);...; \(\left(\begin{array}{c}0\\\vdots\\0\\f_r\end{array}\right)\)
The gradient values are therefore matrices of size N*r, where the gradients of the scalar functions are put in rows:
\(\left(\begin{array}{c}(\nabla f_1)^t\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}(\nabla f_2)^t\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}(\nabla f_r)^t\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}0\\(\nabla f_1)^t\\0\\\vdots\\0\end{array}\right)\); \(\left(\begin{array}{c}0\\(\nabla f_2)^t\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}0\\(\nabla f_r)^t\\0\\\vdots\\0\end{array}\right)\);...; \(\left(\begin{array}{c}0\\\vdots\\0\\(\nabla f_1)^t\end{array}\right)\);...; \(\left(\begin{array}{c}0\\\vdots\\0\\(\nabla f_r)^t\end{array}\right)\)
1.9.1