Émile Parolin
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View article: Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces
Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces Open
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the high-frequency regime. Among the available numerical approa…
Stable approximation of Helmholtz solutions in the 3D ball using evanescent plane waves Open
The goal of this paper is to show that evanescent plane waves are much better at numerically approximating Helmholtz solutions than classical propagative plane waves. By generalizing the Jacobi–Anger identity to complex-valued directions, …
A scalable Domain Decomposition method for Saddle Point problems with GenEO coarse spaces Open
We present an adaptive domain decomposition (DD) preconditioning technique for the solution of saddle point problems with a 2x2 blocks structure. This work utilises the GenEO theory for symmetric positive definite (SPD) problems (Spillane …
Coarse spaces for non-symmetric two-level preconditioners based on local extended generalized eigenproblems Open
Domain decomposition (DD) methods are a natural way to take advantage of parallel computers when solving large scale linear systems. Their scalability depends on the design of the coarse space used in the two-level method. The analysis of …
Stable approximation of Helmholtz solutions in the 3D ball using evanescent plane waves Open
The goal of this paper is to show that evanescent plane waves are much better at numerically approximating Helmholtz solutions than classical propagative plane waves. By generalizing the Jacobi$\unicode{x2013}$Anger identity to complex-val…
Stable approximation of Helmholtz solutions in the disk by evanescent plane waves Open
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of …
Nonlocal optimized schwarz methods for time-harmonic electromagnetics Open
We introduce a new domain decomposition strategy for time harmonic Maxwell’s equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is gu…
Stable approximation of Helmholtz solutions in the disk by evanescent plane waves Open
Superpositions of plane waves are known to approximate well the solutions of the Helmholtz equation. Their use in discretizations is typical of Trefftz methods for Helmholtz problems, aiming to achieve high accuracy with a small number of …
Nonlocal Optimized Schwarz Methods for time-harmonic electromagnetics Open
We introduce a new domain decomposition strategy for time harmonic Maxwell's equations that is valid in the case of automatically generated subdomain partitions with possible presence of cross-points. The convergence of the algorithm is gu…
Matrix form of nonlocal OSM for electromagnetics. Open
The goal of the present paper is twofold. First, we revisit the derivation of the domain decomposition introduced in [Claeys&Parolin,2020] in the acoustic setting, adopting matrix based notations and remaining as explicit as possible. In a…
Non-local Impedance Operator for Non-overlapping DDM for the Helmholtz Equation Open
In the context of time harmonic wave equations, the pioneering work of B. Després [4] has shown that it is mandatory to use impedance type transmission conditions in the coupling of sub-domains in order to obtain convergence of nonoverlapp…
Non-overlapping domain decomposition methods with non-local transmission operators for harmonic wave propagation problems Open
The pioneering work of B. Despres then M. Gander, F. Magoules and F. Nataf have shown that it is mandatory, at least in the context of wave equations, to use impedance type transmission conditions in the coupling of subdomains in order to …
Robust treatment of cross points in Optimized Schwarz Methods Open
In the field of Domain Decomposition (DD), Optimized Schwarz Method (OSM) appears to be one of the prominent techniques to solve large scale time-harmonic wave propagation problems. It is based on appropriate transmission conditions using …
Fast hybrid numerical-asymptotic boundary element methods for high\n frequency screen and aperture problems based on least-squares collocation Open
We present a hybrid numerical-asymptotic (HNA) boundary element method (BEM)\nfor high frequency scattering by two-dimensional screens and apertures, whose\ncomputational cost to achieve any prescribed accuracy remains bounded with\nincrea…
View article: FEM-BEM Coupling for Electromagnetism with the Sparse Cardinal Sine Decomposition,
FEM-BEM Coupling for Electromagnetism with the Sparse Cardinal Sine Decomposition, Open
This paper presents a FEM-BEM coupling method suitable for the numerical simulation of the electromagnetic scattering of objects composed of dielectric materials and perfect electric conduc- tors. The originality of the approach lies in pa…