Adaptive Deflated Multiscale Solvers
D. Boitcov (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Alexander A. Lukyanov – Mentor
C. Vuik – Mentor
Henk Schuttelaars – Graduation committee member
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Abstract
Existing multiscale solvers use a sequence of aggressive restriction, coarse-grid correction and prolongation operators to handle low-frequency modes on the coarse grid. High-frequency errors are resolved by employing a smoother on the fine grid. Deflation preconditioning improves matrix properties, i.e., damps slowly varying errors, corresponding to extreme eigenvalues, in the linear solver residuals. Vari- ous Adapted Deflated Multiscale Solvers are proposed in order to detect the low- frequency modes instead of relying on the residual map and complement today’s stet-of-the-art advanced iterative multiscale strategies.