Finite Difference Based Fast Adaptive Composite Grid Method

摘要

The fast adaptive composite grid (FAC) method is an iterative method for solvingdiscrete boundary value problems on composite grids. In this paper, we consider discrete problems resulting from finite difference discretization on composite grids. We distinguish between two obvious discretization approaches at the grid points on the interfaces between fine and coarse subgrids. The FAC method for solving such discrete problems is described. We study how the convergence behavior depends on these intergrid transfer operators. Based on theoretical insights, (quasi-)optimal intergrid transfer operators are derived. Numerical results illustrate the fast convergence of the FAC method using these intergrid transfer operators.