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06/08/2023
Multilevel domain decomposition-based architectures for physics-informed neural networks
Physics-informed neural networks (PINNs) are a popular and powerful appr...
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11/13/2022
Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
The convergence rate of domain decomposition methods (DDMs) strongly dep...
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11/10/2022
A Trefftz-like coarse space for the two-level Schwarz method on perforated domains
We consider a new coarse space for the ASM and RAS preconditioners to so...
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11/10/2022
Finite basis physics-informed neural networks as a Schwarz domain decomposition method
Physics-informed neural networks (PINNs) [4, 10] are an approach for sol...
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11/09/2022
Solution of time-harmonic Maxwell's equations by a domain decomposition method based on PML transmission conditions
Numerical discretization of the large-scale Maxwell's equations leads to...
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08/03/2022
Scalable Computational Algorithms for Geo-spatial Covid-19 Spread in High Performance Computing
A nonlinear partial differential equation (PDE) based compartmental mode...
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04/20/2022
Closed form optimized transmission conditions for complex diffusion with many subdomains
Optimized transmission conditions in domain decomposition methods have b...
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02/17/2022
Are spectral coarse spaces sufficiently robust for heterogeneous Helmholtz problems?
Numerical solution of heterogeneous Helmholtz problems presents various ...
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10/26/2021
Overlapping Schwarz methods with GenEO coarse spaces for indefinite and non-self-adjoint problems
GenEO ('Generalised Eigenvalue problems on the Overlap') is a method for...
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03/31/2021
Inexact subdomain solves using deflated GMRES for Helmholtz problems
We examine the use of a two-level deflation preconditioner combined with...
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03/30/2021
GenEO coarse spaces for heterogeneous indefinite elliptic problems
Motivated by recent work on coarse spaces for Helmholtz problems, we pro...
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03/14/2021
Optimizing transmission conditions for multiple subdomains in the Magnetotelluric Approximation of Maxwell's equations
Classically transmission conditions between subdomains are optimized for...
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03/10/2021
Several ways to achieve robustness when solving wave propagation problems
Wave propagation problems are notoriously difficult to solve. Time-harmo...
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12/04/2020
A comparison of coarse spaces for Helmholtz problems in the high frequency regime
Solving time-harmonic wave propagation problems in the frequency domain ...
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12/04/2020
Two-level DDM preconditioners for positive Maxwell equations
In this paper we develop and analyse domain decomposition methods for li...
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06/15/2020
Analysis of parallel Schwarz algorithms for time-harmonic problems using block Toeplitz matrices
In this work we study the convergence properties of the one-level parall...
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04/14/2020
Iterative frequency-domain seismic wave solvers based on multi-level domain-decomposition preconditioners
Frequency-domain full-waveform inversion (FWI) is suitable for long-offs...
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12/12/2019
On the Dirichlet-to-Neumann coarse space for solving the Helmholtz problem using domain decomposition
We examine the use of the Dirichlet-to-Neumann coarse space within an ad...
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06/29/2017