Hybrid Multigrid/Schwarz Algorithms for the Spectral Element Method

TitleHybrid Multigrid/Schwarz Algorithms for the Spectral Element Method
Publication TypeReport
Year of Publication2003
AuthorsLottes, JW, Fischer, PF
Series TitleJ. Sci. Comput.
Date Published04/2003
Other NumbersANL/MCS-P1052-0403

<p>We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson equation. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the originating SE matrices converge faster than FE-based methods and that weighting the Schwarz matrices by the inverse of the diagonal counting matrix is essential to effective Schwarz smoothing. Several of the methods considered achieve convergence rates comparable to those attained by classic multigrid on regular grids.</p>