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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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LEPNC scheme for diffusion equation \(u - \div(K \nabla(\zeta(u))) = f\). More...
#include <LEPNC_StefanPME.hpp>
Public Types | |
| using | solution_function_type = std::function< double(double, double)> |
| type for solution | |
| using | source_function_type = std::function< double(double, double, Cell *)> |
| type for source | |
| using | grad_function_type = std::function< VectorRd(double, double, Cell *)> |
| type for gradient | |
| using | tensor_function_type = std::function< Eigen::Matrix2d(double, double, Cell *)> |
| type for diffusion tensor | |
Public Member Functions | |
| LEPNC_StefanPME (LEPNCCore &nc, tensor_function_type kappa, size_t deg_kappa, source_function_type source, BoundaryConditions BC, solution_function_type exact_solution, grad_function_type grad_exact_solution, TestCaseNonLinearity::nonlinearity_function_type zeta, double weight, std::string solver_type, std::ostream &output=std::cout) | |
| Constructor of the class. | |
| Eigen::VectorXd | solve () |
| Assemble and solve the scheme. | |
| Eigen::VectorXd | apply_nonlinearity (const Eigen::VectorXd &Y, const std::string type) const |
| Compute non-linearity on vector (depends if weight=0, weight=1 or weight\in (0,1) ) | |
| double | L2_MassLumped (const Eigen::VectorXd Xh) const |
| Mass-lumped L2 norm of a function given by a vector. | |
| double | EnergyNorm (const Eigen::VectorXd Xh) const |
| Discrete energy norm (associated to the diffusion operator) | |
| double | get_assembly_time () const |
| cpu time to assemble the scheme | |
| double | get_solving_time () const |
| cpu time to solve the scheme | |
| double | get_solving_error () const |
| residual after solving the scheme | |
| double | get_itime (size_t idx) const |
| various intermediate assembly times | |
LEPNC scheme for diffusion equation \(u - \div(K \nabla(\zeta(u))) = f\).
The vector Xh manipulated in the resolution has mixed components, corresponding either to the unknown u or to \(\zeta(u)\), depending on the choice of weight of mass-lumping for the cell/edge unknowns. If no weight is put on the edges (resp. the cells), then the edge (resp. cell) unknowns represent \(\zeta(u)\). Otherwise, they represent u.
1.9.8