Grid Generation

This example shows how to initialize a DataMatrix object, store it to a file and then to restore it back.

Configuring the Grid

Start with defining the dimensionality of the grid. This is done by modifying the configuration file located at:

"library/source/abbrevi.h"

Example definition:

#define DimensionSparseGrid 2

Regular sparse grid

This example initializes a regular sparse grid, using the class AdaptiveSparseGrid, refines it recursively around a center point, and outputs its structure in both textual and GNU plotting formats. It illustrates how to:

• Define the refinement level of the grid.
• Add recursive sons (children) of a given point.
• Print grid points at specified levels.
• Export the grid structure for visualization.

#include "source/sparseEXPDE.h"
 
int main(int argc, char **argv) {
 
    AdaptiveSparseGrid regular_grid;
 
    int level=3;
    IndexDimension centerPoint;
 
    regular_grid.AddRecursiveSonsOfPoint(centerPoint,level);
 
    regular_grid.PrintActiveHanging(level);
    regular_grid.PrintActiveHanging(2);
    regular_grid.Print_gnu("grid.gnu");
 
    return 0;
}

Adaptive Sparse Grid

Next, we want to generate an adaptive sparse grid. Let us do this in more detail. We start by initializing an adaptive sparse grid, defining grid points (IndexDimension) and adding them to our grid.

#include "source/sparseEXPDE.h"
 
int main(int argc, char **argv) {
 
    AdaptiveSparseGrid adaptiveSparseGrid;
    int level = 3;
 
 
    IndexDimension centerPoint;
    IndexDimension bottomLeft = centerPoint.leftSon(0).leftSon(1).leftSon(0).leftSon(1);
    IndexDimension topRight = centerPoint.rightSon(0).rightSon(1).rightSon(0).rightSon(1);
 
    adaptiveSparseGrid.AddPoint(bottomLeft);
    adaptiveSparseGrid.AddPoint(topRight);

In order to perform a Matrix-Vector-Multiplication on such a grid, we need to add grid points.

This is done as follows:

    adaptiveSparseGrid.completeDirichletGrid();

Finally we can export the grid structure.

 
 
    adaptiveSparseGrid.PrintActiveHanging(level);
    adaptiveSparseGrid.Print_gnu("grid.gnu");
    adaptiveSparseGrid.Print_vtk("grid.vtk");
 
    cout << adaptiveSparseGrid.getDOFS() << "  " << adaptiveSparseGrid.getHangingNodes() << endl;
 
    return 0;
}