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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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Scalar monomial basis on a face. More...
#include <basis.hpp>
Public Types | |
| typedef double | FunctionValue |
| typedef VectorRd | GradientValue |
| typedef VectorRd | CurlValue |
| typedef double | DivergenceValue |
| typedef MatrixRd | HessianValue |
| typedef Face | GeometricSupport |
| typedef Eigen::Matrix< double, 2, dimspace > | JacobianType |
Public Member Functions | |
| MonomialScalarBasisFace (const Face &F, size_t degree) | |
| Constructor. More... | |
| size_t | dimension () const |
| Dimension of the basis. More... | |
| FunctionValue | function (size_t i, const VectorRd &x) const |
| Evaluate the i-th basis function at point x. More... | |
| GradientValue | gradient (size_t i, const VectorRd &x) const |
| Evaluate the gradient of the i-th basis function at point x. More... | |
| CurlValue | curl (size_t i, const VectorRd &x) const |
| Evaluate the two-dimensional curl of the i-th basis function at point x. More... | |
| HessianValue | hessian (size_t i, const VectorRd &x) const |
| Evaluate the Hessian of the i-th basis function at point x. More... | |
| size_t | max_degree () const |
| Returns the maximum degree of the basis functions. More... | |
| const VectorRd & | normal () const |
| Return the normal to the face used in the computation of the curl. More... | |
| const JacobianType & | jacobian () const |
| Return the Jacobian of the coordinate system transformation. More... | |
| const JacobianType | coordinates_system () const |
| Return the system of coordinates (basis in rows) on the face. More... | |
| Eigen::Vector2i | powers (size_t i) const |
| Returns the powers of the i-th basis function (its degree can be found using powers(i).sum()) More... | |
Static Public Attributes | |
| constexpr static const TensorRankE | tensorRank = Scalar |
| constexpr static const bool | hasAncestor = false |
| static const bool | hasFunction = true |
| static const bool | hasGradient = true |
| static const bool | hasCurl = true |
| static const bool | hasDivergence = false |
| static const bool | hasHessian = true |
| static const bool | hasCurlCurl = false |
Scalar monomial basis on a face.
1.9.1