SGMGA_COEFFICIENT:
The "Combinatorial Coefficient" for Anisotropic Sparse Grids

This short paper is an attempt to outline the changes that must be made when moving from the computation of an isotropic sparse grid to an anisotropic sparse grid, that is, a sparse grid which can be designed to achieve greater precision in particular spatial dimensions. The main changes to the algorithm involve the procedure for selecting which product grids are eligible, and the evaluation of the appropriate weighting coefficient. For isotropic grids, this weighting coefficient is a signed combinatorial coefficient. For anisotropic grids, the computation of this coefficient is significantly different. The paper discusses two formulations of this procedure (which turn out to be the same, but simply using different notations), and works out the construction process for a simple 2D example.

A PDF version of the is available in ../../presentations/sgmga_coefficient.pdf.

The following files constitute the LaTeX file used to create the slides:

• boxes_level0.png, a box plot for level 0 of the example sparse grid.
• boxes_level1.png, a box plot for level 1 of the example sparse grid.
• boxes_level2.png, a box plot for level 2 of the example sparse grid.
• boxes_level3.png, a box plot for level 3 of the example sparse grid.
• boxes_level4.png, a box plot for level 4 of the example sparse grid.
• boxes_level5.png, a box plot for level 5 of the example sparse grid.
• sgmga_coefficient.tex, the main LaTeX file;

You can go up one level to the LATEX home page.