Optimized Schwarz Methods with Robin Conditions for the Advection-Diffusion Equation
We study optimized Schwarz methods for the stationary advectiondiffusion equation in two dimensions. We look at simple Robin transmission conditions, with one free parameter. In the nonoverlapping case, we solve exactly the associated min-max problem to get a direct formula for the optimized parameter. In the overlapping situation, we solve only an approximate min-max problem. The asymptotic performance of the resulting methods, for small mesh sizes, is derived. Numerical experiments illustrate the improved convergence compared to other Robin conditions.
KeywordsUnique Minimizer Domain Decomposition Method Asymptotic Performance Convergence Factor Schwarz Method
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