Seminar in Numerical Analysis: Frédéric Nataf (CNRS Paris 6)
Optimized Schwarz methods (OSM) are very popular methods which were introduced by P.L. Lions for elliptic problems and B. Despres for propagative wave phenomena. One drawback is the lack of theoretical results for variable coefficients problems and overlapping decompositions. We build here a coarse space for which the convergence rate of the two-level method is guaranteed regardless of the regularity of the coefficients. We do this by introducing a symmetrized variant of the ORAS (Optimized Restricted Additive Schwarz) algorithm. Numerical results on nearly incompressible elasticity and Stokes system are shown for systems with hundred of millions of degrees of freedom on high performance computers.
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