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Domain Decomposition for Differential Equations

Mary Wheeler, Clint Dawson, Ivan Yotov, Mónica Martínez

Presented at the 1997 CRPC Annual Meeting

In this tutorial, domain decomposition methodology will be introduced by first considering two-point boundary value problems. Extensions to a time-dependent nonlinear example will also be discussed. For multidimensional partial differential equations, parallel domain decomposition solvers (balancing and multigrid for nonoverlapping domains and additive Schwarz for overlapping domains) will be formulated and parallel scaling results presented. Additional topics will include application of domain decomposition solution methods to non-matching grids and nonlinear flow problems and to preprocessors for hydrodynamic flow and and transport.