sgpp::pde::LaplaceUpPrewavelet Class Reference

Implements the down Method needed for the Laplace operator on prewavelet grids. More...

#include <LaplaceUpPrewavelet.hpp>

Public Member Functions
	LaplaceUpPrewavelet (sgpp::base::GridStorage *storage)
	Constructor. More...
void	operator() (sgpp::base::DataVector &source, sgpp::base::DataVector &result, grid_iterator &index, size_t dim)
	This operations performs the calculation of down in the direction of dimension dim More...
	~LaplaceUpPrewavelet ()
	Destructor. More...

Protected Types
typedef sgpp::base::GridStorage::grid_iterator	grid_iterator

Protected Attributes
sgpp::base::GridStorage *	storage
	Pointer to sgpp::base::GridStorage object. More...

Detailed Description

Implements the down Method needed for the Laplace operator on prewavelet grids.

Here, the prewavlets have an advantage over the normal linear base due to the semi othogonality. That means, for the calculation, only the gridpoint in the same level have to be taken into account. The matrix entries are the following:

\begin{eqnarray*} m_{(1,1)(1,1)}&=&\frac{1}{3}\\m_{(2,1)(2,3)}&=&\frac{1}{25}\\m_{(l,1)(l,1)}&=&m_{(l,2^{l}-1)(l,2^{l}-1)}=\frac{44}{75}h_{l}\\m_{(l,1)(l,3)}&=&m_{(l,2^{l}-1)(l,2^{l}-3)}=\frac{11}{75}h_{l}\\m_{(l,i)(l,i)}&=&\frac{18}{25}h_{l}\\m_{(l,i)(l,i\pm2)}&=&\frac{2}{15}h_{l}\\m_{(l,i)(l,i\pm4)}&=&-\frac{11}{75}h_{l} \end{eqnarray*}

With that, the calculation of the entire matrix is completed, thus no additional up-part is needed.

Member Typedef Documentation

grid_iterator

typedef sgpp::base::GridStorage::grid_iterator sgpp::pde::LaplaceUpPrewavelet::grid_iterator

protected

Constructor & Destructor Documentation

LaplaceUpPrewavelet()

sgpp::pde::LaplaceUpPrewavelet::LaplaceUpPrewavelet ( sgpp::base::GridStorage *  storage )

explicit

Constructor.

Parameters

storage

the grid's sgpp::base::GridStorage object

~LaplaceUpPrewavelet()

sgpp::pde::LaplaceUpPrewavelet::~LaplaceUpPrewavelet

(

)

Destructor.

Member Function Documentation

operator()()

void sgpp::pde::LaplaceUpPrewavelet::operator()	(	sgpp::base::DataVector &	source,
		sgpp::base::DataVector &	result,
		grid_iterator &	index,
		size_t	dim
	)

This operations performs the calculation of down in the direction of dimension dim

Parameters

source	sgpp::base::DataVector that contains the gridpoint's coefficients (values from the vector of the laplace operation)
result	sgpp::base::DataVector that contains the result of the up operation
index	a iterator object of the grid
dim	current fixed dimension of the 'execution direction'

References sgpp::base::HashGridIterator::get(), h, sgpp::base::HashGridIterator::hintLeft(), sgpp::base::HashGridIterator::hintRight(), python.statsfileInfo::i, sgpp::base::HashGridStorage::isInvalidSequenceNumber(), sgpp::base::HashGridIterator::seq(), sgpp::base::HashGridIterator::set(), and storage.

Member Data Documentation

storage

sgpp::base::GridStorage* sgpp::pde::LaplaceUpPrewavelet::storage

protected

Pointer to sgpp::base::GridStorage object.

Referenced by operator()().

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

• pde/src/sgpp/pde/basis/prewavelet/algorithm_sweep/LaplaceUpPrewavelet.hpp
• pde/src/sgpp/pde/basis/prewavelet/algorithm_sweep/LaplaceUpPrewavelet.cpp