Line data    Source code

       1           0 : // Distributed under the MIT License.
       2             : // See LICENSE.txt for details.
       3             : 
       4             : #pragma once
       5             : 
       6             : #include <cstddef>
       7             : 
       8             : /// \cond
       9             : class Matrix;
      10             : template <size_t>
      11             : class Mesh;
      12             : namespace Spectral {
      13             : enum class Basis : uint8_t;
      14             : enum class Quadrature : uint8_t;
      15             : }  // namespace Spectral
      16             : /// \endcond
      17             : 
      18             : namespace Spectral {
      19             : /*!
      20             :  * \brief %Matrix used to transform from the nodal coefficients of a function to
      21             :  * its spectral coefficients (modes). Also referred to as the inverse
      22             :  * _Vandermonde matrix_.
      23             :  *
      24             :  * \details This is the inverse to the Vandermonde matrix \f$\mathcal{V}\f$
      25             :  * computed in modal_to_nodal_matrix(size_t). It can be computed
      26             :  * analytically for Gauss quadrature by evaluating
      27             :  * \f$\sum_j\mathcal{V}^{-1}_{ij}u_j=\widetilde{u}_i=
      28             :  * \frac{(u,\Phi_i)}{\gamma_i}\f$
      29             :  * for a Lagrange basis function \f$u(x)=l_k(x)\f$ to find
      30             :  * \f$\mathcal{V}^{-1}_{ij}=\mathcal{V}_{ji}\frac{w_j}{\gamma_i}\f$ where the
      31             :  * \f$w_j\f$ are the Gauss quadrature weights and \f$\gamma_i\f$ is the norm
      32             :  * square of the spectral basis function \f$\Phi_i\f$.
      33             :  *
      34             :  * \param num_points The number of collocation points
      35             :  *
      36             :  * \see modal_to_nodal_matrix(size_t)
      37             :  */
      38             : template <Basis BasisType, Quadrature QuadratureType>
      39           1 : const Matrix& nodal_to_modal_matrix(size_t num_points);
      40             : 
      41             : /*!
      42             :  * \brief Transformation matrix from nodal to modal coefficients for a
      43             :  * one-dimensional mesh.
      44             :  *
      45             :  * \see nodal_to_modal_matrix(size_t)
      46             :  */
      47           1 : const Matrix& nodal_to_modal_matrix(const Mesh<1>& mesh);
      48             : }  // namespace Spectral