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Energy-minimizing coarse spaces for two-level Schwarz methods for multiscale PDEs. (English) Zbl 1224.65292
The authors compare different choices of coarse spaces for two-level overlapping Schwarz-type domain decomposition methods, applied to second-order elliptic boundary problems with highly varying coefficients. A construction of the coarse space based on energy minimization is proposed and its efficient implementation is described on a model scalar problem of stationary heat conduction type. Numerical experiments on a 2D model problem show that the proposed coarse space outperforms in scalability and robustness other investigated choices of coarse spaces. However, some examples are presented for which the proposed method is not robust with respect to coefficient variation.

MSC:
 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure 65Y05 Parallel numerical computation
GAUSSIAN
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