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An introduction to domain decomposition methods - algorithms, theory, and parallel implementation

The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts.
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Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

This work introduces in a variational setting a new coarse space that is robust even when there are such heterogeneities in the PDE coefficients, by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence.
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Optimized Schwarz Methods for Maxwell's Equations

It is shown here why the classical Schwarz method applied to both the time harmonic and time discretized Maxwell's equations converges without overlap: the method has the same convergence factor as a simple optimized Schwarz method for a scalar elliptic equation.
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Analysis of a Two-level Schwarz Method with Coarse Spaces Based on Local Dirichlet-to-Neumann Maps

This work presents a rigorous analysis of a two-level overlapping additive Schwarz method, which provides an automatic criterion for the number of modes that need to be added per subdomain to obtain a convergence rate of the order of the constant coefficient case.
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Locally implicit discontinuous Galerkin method for time domain electromagnetics

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A Coarse Space Construction Based on Local Dirichlet-to-Neumann Maps

This work construct coarse-grid space using the low-frequency modes of the subdomain Dirichlet-to-Neumann maps and apply the obtained two-level preconditioners to the extended or the original linear system arising from an overlapping domain decomposition.
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Numerical Modeling and High-Speed Parallel Computing: New Perspectives on Tomographic Microwave Imaging for Brain Stroke Detection and Monitoring.

This article deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Iterative microwave tomographic imaging requires the…
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Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method

This paper obtains a preconditioner called RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN, but with all components directly defined by the iterative method, and has the advantage that RasPEN already converges when used as an iterative solver, in contrast to ASIN.
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Microwave tomography for brain stroke imaging

This paper deals with microwave tomography for brain stroke imaging using state-of-the-art numerical modeling and massively parallel computing. Iterative microwave tomographic imaging requires the…
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A domain decomposition approach to finite volume solutions of the Euler equations on unstructured triangular meshes

This study reports on the formulation and the evaluation of a domain decomposition algorithm for the parallel solution of two‐dimensional compressible inviscid flows and formulate an additive Schwarz algorithm using appropriate matching conditions at the subdomain interfaces.
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