# 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…

## 4 Citations

### A fully algebraic and robust two-level Schwarz method based on optimal local approximation spaces

- Mathematics, Computer ScienceArXiv
- 2022

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.

### Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems

- MathematicsIMA Journal of Numerical Analysis
- 2022

An iterative solver which is efficient in parallel and very effective for a wide range of convection–diffusion– reaction problems, and whose discretisations are solved with preconditioned GMRES.

### Efficient Algebraic Two-Level Schwarz Preconditioner For Sparse Matrices

- Computer Science, MathematicsArXiv
- 2022

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.

### Scalable multiscale-spectral GFEM for composite aero-structures

- Computer Science
- 2022

By allowing low-cost approximate solves for closely related models or geometries this e-cient, novel technology provides the basis for future applications in optimisation or uncertainty quantiﬁcation on challenging problems in composite aero-structures.

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