Implementation for Bspline functions of Laplace Operation, bspline grids without boundaries. More...

#include <OperationLaplaceBspline.hpp>

Inheritance diagram for sgpp::pde::OperationLaplaceBspline:

Public Member Functions
virtual void	mult (sgpp::base::DataVector &alpha, sgpp::base::DataVector &result)
	Implementation of standard matrix multiplication. More...

	OperationLaplaceBspline (sgpp::base::Grid *grid)
	Constructor that creates an own matrix i.e. More...

virtual	~OperationLaplaceBspline ()
	Destructor. More...

Public Member Functions inherited from sgpp::base::OperationMatrix
	OperationMatrix ()
	Constructor. More...

virtual	~OperationMatrix ()
	Destructor. More...

Detailed Description

Implementation for Bspline functions of Laplace Operation, bspline grids without boundaries.

Constructor & Destructor Documentation

◆ OperationLaplaceBspline()

sgpp::pde::OperationLaplaceBspline::OperationLaplaceBspline ( sgpp::base::Grid * grid )

explicit

Constructor that creates an own matrix i.e.

matrix is destroyed by the destructor of OperationLaplaceBspline

Parameters

grid	the sparse grid

◆ ~OperationLaplaceBspline()

sgpp::pde::OperationLaplaceBspline::~OperationLaplaceBspline ( )

virtual

Destructor.

Member Function Documentation

◆ mult()

void sgpp::pde::OperationLaplaceBspline::mult	(	sgpp::base::DataVector &	alpha,
		sgpp::base::DataVector &	result
	)

virtual

Implementation of standard matrix multiplication.

Parameters

alpha	DataVector that is multiplied to the matrix
result	DataVector into which the result of multiplication is stored

int nabla phi_i(x) * nabla phi_j(x) dx = sum_k int (dx_k phi_i(x)) * (dx_k phi_j(x)) dx = sum_k int (phi'_{i_k}(x_k) * phi'_{i_k}(x_k) * prod_{l!=k} phi_{i_l}(x_l) * phi_{j_l}(x_l)) dx = sum_k int (phi'_{i_k}(x_k) * phi'_{j_k}(x_k)) dx_k * prod_{l!=k} int (phi_{i_l}(x_l) * phi_{j_l}(x_l)) dx_l

Implements sgpp::base::OperationMatrix.

References sgpp::base::BsplineBasis< LT, IT >::eval(), sgpp::base::BsplineBasis< LT, IT >::evalDx(), sgpp::base::Grid::getBasis(), python.uq.operations.sparse_grid::getDegree(), sgpp::base::Grid::getDimension(), sgpp::base::GaussLegendreQuadRule1D::getLevelPointsAndWeightsNormalized(), sgpp::base::HashGridStorage::getSize(), sgpp::base::DataVector::getSize(), sgpp::base::Grid::getSize(), sgpp::base::Grid::getStorage(), python.statsfileInfo::i, python.utils.statsfile2gnuplot::j, friedman::p, and python.leja::start.

The documentation for this class was generated from the following files: