Two-level Overlapping Schwarz Preconditioners with Algebraic Multiscale Coarse Spaces for Large-scale Heterogeneous Problems
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The discretization of large, heterogeneous elliptic problems yields ill-conditioned linear systems that hinder the convergence of Krylov subspace methods. In addition, parallel scalability is negatively affected, resulting in poor efficiency for large-scale problems. The two-level overlapping additive Schwarz method provides a robust and scalable preconditioning scheme for such problems. A crucial component of the preconditioner is the coarse space spanning the global coupling problem. An effective coarse space represents the problematic error modes, ensuring robustness and scalability for different coefficient distributions. In this talk, we examine an algebraic multiscale coarse space based on the Algebraic Multiscale Solver (AMS) and its parallel implementation in the FROSch (Fast and Robust Overlapping Schwarz) package within the Trilinos software toolkit. We also investigate techniques to enhance both the preconditioner’s robustness and computational efficiency. Finally, we compare the parallel performance of our algebraic multiscale coarse space with other algebraic coarse space options available in FROSch. We show that the algebraic multiscale approach is robust for a wide range of high coefficient contrast problems, exhibiting good scalability where other coarse spaces do not.
