An Energy-Minimizing Interpolation for Multigrid Methods

Wing-Lok Wan

Department of Mathematics
University of California
Los Angeles, CA 90095-1555


We shall study multigrid methods from energy minimizations and approximations. Through the analysis of an multigrid method in 1D, we introduce the concepts of stability and the approximation property in the classical theory. Based on them, we derive an energy-minimizing interpolation and present a two level analysis for it. Issues on coarsening are also addressed. Finally, we demonstrate the effectiveness of the multigrid method by applying it to unstructured grids computations and discontinuous coefficient problems.