Multigrid Method Based on Incomplete Gaussian Elimination

摘要

In this paper, we introduce and analyze a new Schur complement approximationbased on incomplete Gaussian elimination. The approximate Schur complement is used to develop a multigrid method. This multigrid method has an algorithmic structure that is very similar to the algorithmic structure of classical multigrid methods. The resulting method is almost purely algebraic and has interesting robustness properties with respect to variation in problem parameters.