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Session S20 - Applied Math and Computational Methods and Analysis across the Americas

Friday, July 16, 14:30 ~ 15:00 UTC-3

Additive Schwarz Preconditioners for a Localized Orthogonal Decomposition Method

José Garay

Louisiana State University, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The solution of multiscale elliptic PDEs with non-separable scales and high contrast in the coefficients by standard Finite Element Methods (FEM) is typically prohibitively expensive since it requires the resolution of all characteristic lengths to produce an accurate solution. Numerical homogenization methods such as Localized Orthogonal Decomposition (LOD) methods provide access to feasible and reliable simulations of such multiscale problems. These methods are based on the idea of a generalized finite element space where the generalized basis functions are obtained by modifying standard coarse FEM basis functions to incorporate relevant microscopic information in a computationally feasible procedure. Using this enhanced basis one can solve a much smaller problem to produce an approximate solution whose accuracy is comparable to the solution obtained by the expensive standard FEM. We present a variant of LOD that uses domain decomposition techniques to compute the basis corrections and we also provide a two-level preconditioner for the resulting linear system.

Joint work with Susanne C. Brenner (Louisiana State University, United States) and Li-yeng Sung (Louisiana State University, United States).

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