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Achieving robustness in domain decomposition

Domain Decomposition methods are a family of solvers tailored to very large linear systems that require parallel computers. They proceed by splitting the computational domain into subdomains and then approximating the inverse of the original problem with local inverses coming from the subdomains. I will present some classical domain decomposition methods and show that for realistic simulations (with heterogeneous materials for instance) convergence usually becomes very slow. Then I will explain how this can be fixed by injecting more information into the solver, either by adding a coarse space (this is also known as deflation) or by using multiple search directions within the conjugate gradient algorithm.

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