SG++-Doxygen-Documentation
sgpp::base::ConvertLinearToPrewavelet Class Reference

Class that implements the transformation of a hierarchical linear sparse grid to a hierarchical prewavelet sparse grid. More...

#include <ConvertLinearToPrewavelet.hpp>

Public Member Functions

 ConvertLinearToPrewavelet (GridStorage &storage, GridStorage &shadowstorage)
 Constructor, must be bind to a grid. More...
 
void operator() (DataVector &source, DataVector &result, grid_iterator &index, size_t dim)
 Converts a given linear base to a prewavelet base. More...
 
 ~ConvertLinearToPrewavelet ()
 Destructor. More...
 

Protected Types

typedef GridStorage::grid_iterator grid_iterator
 
typedef index_t index_type
 
typedef level_t level_type
 

Protected Attributes

GridStorageshadowstorage
 
GridStoragestorage
 the grid object More...
 

Detailed Description

Class that implements the transformation of a hierarchical linear sparse grid to a hierarchical prewavelet sparse grid.

Therefore the ()operator is implemented in order to use the sweep algorithm for the grid traversal. Let the coefficients from the hat basis be \( h_{l,i}\) and from the prewavelet basis \( u_{l,i} \). To calculate the surplusses, temp values are needed:

\[ (l,i)\neq G_{n}^{1}:t_{l,i}=-\frac{6}{10}u_{l,i\pm1}+t_{l+1,2i} \]

All temp values for levels greater than the maximal level of the grid are set to 0. The actual transformation is defined by the following tridiagonal equation system:

\begin{eqnarray*} \frac{16}{10}u_{l,i}+\frac{4}{10}u_{l,i\pm2}&=&h_{l,i}-t_{l+1,2i}+\frac{1}{2}t_{l+1,2(i\pm1)}\\\frac{12}{10}u_{l,1}+\frac{4}{10}u_{l,3}&=&h_{l,1}-t_{l+1,2}+\frac{1}{2}t_{l+1,4}\\\frac{12}{10}u_{l,2^{l}-1}+\frac{4}{10}u_{l,2^{l}-3}&=&h_{l,2^{l}-1}-t_{l+1,2(2^{l}-1)}+\frac{1}{2}t_{l+1,2(2^{l}-2)} \end{eqnarray*}

For solving these tridiagonal systems, the method described in http://www.nrbook.com/a/bookcpdf/c2-4.pdf was used. Some odd Fileopen® plugin is needed to open that file ... sorry for that! the picture depicts all needed variables in oder to perform the transformation:

prewavelets_hierarch.png
This picture shows all involved gridpoints (red crosses) and temp values (green circles) to calculate the new hierarchical coefficients (red arrows) and new temp values (green arrows).

Member Typedef Documentation

Constructor & Destructor Documentation

sgpp::base::ConvertLinearToPrewavelet::ConvertLinearToPrewavelet ( GridStorage storage,
GridStorage shadowstorage 
)
inline

Constructor, must be bind to a grid.

An adaptive grid with prewavelet ansatz functions requires for operations using the up-down algorithm shadow points. These shadow points a needed just for data transport, thus they do not have an influence on the final function. Please refer to sgpp::pde::UpDownOneOpDimWithShadow for more information.

Parameters
storagethe grid storage object of the the grid, on which the hierarchisation should be executed
shadowstorageshadow points (see detailed description)
sgpp::base::ConvertLinearToPrewavelet::~ConvertLinearToPrewavelet ( )
inline

Destructor.

References chess::dim, and operator()().

Member Function Documentation

Member Data Documentation

GridStorage& sgpp::base::ConvertLinearToPrewavelet::shadowstorage
protected
GridStorage& sgpp::base::ConvertLinearToPrewavelet::storage
protected

the grid object

Referenced by operator()().


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