sgmga_coefficient_2010_vt

sgmga_coefficient_2010_vt, "The Combinatorial Coefficient for Anisotropic Sparse Grids", outlines the changes to be made when moving from 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. This document was written at Virginia Tech in 2010.

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.

• sgmga_coefficient_2010_vt.tex
• sgmga_coefficient_2010_vt.pdf

The following files were used to create this document:

• 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.