Print Email Facebook Twitter Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods Title Adaptive GDSW Coarse Spaces of Reduced Dimension for Overlapping Schwarz Methods Author Heinlein, A. (TU Delft Delft Institute of Applied Mathematics; TU Delft Numerical Analysis) Klawonn, Axel (University of Cologne) Knepper, Jascha (University of Cologne) Rheinbach, Oliver (University of Technology Bergakademie Freiberg) Widlund, Olof B. (Courant Institute of Mathematical Sciences) Department Delft Institute of Applied Mathematics Date 2022 Abstract A new reduced-dimension adaptive generalized Dryja-Smith-Widlund (GDSW) overlapping Schwarz method for linear second-order elliptic problems in three dimensions is introduced. It is robust with respect to large contrasts of the coefficients of the partial differential equations. The condition number bound of the new method is shown to be independent of the coefficient contrast and only dependent on a user-prescribed tolerance. The interface of the nonoverlapping domain decomposition is partitioned into nonoverlapping patches. The new coarse space is obtained by selecting a few eigenvectors of certain local eigenproblems which are defined on these patches. These eigenmodes are energy-minimally extended to the interior of the nonoverlapping subdomains and added to the coarse space. By using a new interface decomposition, the reduced-dimension adaptive GDSW overlapping Schwarz method usually has a smaller coarse space than existing GDSW and adaptive GDSW domain decomposition methods. A robust condition number estimate is proven for the new reduced-dimension adaptive GDSW method which is also valid for existing adaptive GDSW methods. Numerical results for the equations of isotropic linear elasticity in three dimensions confirming the theoretical findings are presented. Subject adaptive coarse spacesdomain decompositionGDSWmultiscaleoverlapping Schwarzreduced dimension To reference this document use: http://resolver.tudelft.nl/uuid:60e1aa6d-3aa8-4081-8754-978646c3f6b1 DOI https://doi.org/10.1137/20M1364540 ISSN 1064-8275 Source SIAM Journal on Scientific Computing, 44 (3), A1176-A1204 Part of collection Institutional Repository Document type journal article Rights © 2022 A. Heinlein, Axel Klawonn, Jascha Knepper, Oliver Rheinbach, Olof B. Widlund Files PDF 20m1364540.pdf 4.36 MB Close viewer /islandora/object/uuid:60e1aa6d-3aa8-4081-8754-978646c3f6b1/datastream/OBJ/view