# Multilevel Spectral Domain Decomposition

@article{Bastian2022MultilevelSD, title={Multilevel Spectral Domain Decomposition}, author={Peter Bastian and Robert Scheichl and Linus Seelinger and Arne Strehlow}, journal={ArXiv}, year={2022}, volume={abs/2106.06404} }

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer from severe memory requirements and limited parallel scalability, while iterative solvers in general lack robustness. Two-level spectral domain decomposition methods can provide such robustness for symmetric positive definite linear systems, by using coarse…

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## 3 Citations

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A novel algebraic adaptive coarse space, which relies on the a -orthogonal decomposition of (local) ﬁnite element (FE) spaces into functions that solve the partial dif-ferential equation (PDE) with some trace and FE functions that are zero on the boundary, is proposed.

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A new spectral coarse space that can be constructed in a fully-algebraic way unlike most existing spectral coarse spaces is presented and theoretical convergence result for Hermitian positive definite diagonally dominant matrices is presented.

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