A SPARSE GRID DISCRETIZATION OF THE HELMHOLTZ EQUATION WITH VARIABLE CO EFFICIENTS IN HIGH DIMENSIONS

摘要

The computational effort for solving elliptic differential equations can significantly be reduced by using sparse grids. We present a new Ritz-Galerkin discretization of the Helmholtz equation with variable coefficients on sparse grids. This discretization uses prewavelets and a semi-orthogonality property on sparse grids. A detailed convergence analysis is given for the arbitrary dimension d. The linear equation system of the discretization can efficiently be solved by a multigrid Q-cycle.