Multilevel Schwarz Methods for Elliptic Partial Differential Equations


Advanced Numerical Methods for Scientific Computing
Multilevel Schwarz Methods for Elliptic Partial Differential Equations
Monday 8th November 2010
Migliorati, Giovanni; Quarteroni, Alfio
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We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic Partial Di fferential Equations by the fiite element method. In our analysis we deal with unstructured mesh partitions and with subdomain boundaries resulting from using the mesh partitioner. We start from two-level preconditioners with either aggregative or interpolative coarse level components, then we focus on a strategy to increase the number of levels. For all preconditioners, we consider the additive residual update and its multiplicative variants within and between levels. Moreover, we compare the preconditioners behaviour, regarding scalability and rate of convergence. Numerical results are provided for elliptic boundary-value problems, including a convection-di ffusion problem when suitable stabilization becomes necessary.