7 citations · 23 across the 17 of their papers we have counts for
19 papers
Boundary Element Methods for the Laplace Hypersingular Integral Equation on Multiscreens: a two-level Substructuring Preconditioner
Martin Averseng, Xavier Claeys, Ralf Hiptmair
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a -dimensional triangulated…
Multi-domain FEM-BEM coupling for acoustic scattering
Marcella Bonazzoli, Xavier Claeys
We model time-harmonic acoustic scattering by an object composed of piece-wise homogeneous parts and an arbitrarily heterogeneous part. We propose and analyze new formulations that…
Non-local optimized Schwarz method with physical boundaries
Xavier Claeys
We extend the theoretical framework of non-local optimized Schwarz methods as introduced in [Claeys,2021], considering an Helmholtz equation posed in a bounded cavity supplemented…
Fractured Meshes
Martin Averseng, Xavier Claeys, Ralf Hiptmair
This work introduces ``generalized meshes", a type of meshes suited for the discretization of partial differential equations in non-regular geometries. Generalized meshes extend re…
How does the partition of unity influence SORAS preconditioner?
Marcella Bonazzoli, Xavier Claeys, Frédéric Nataf +1
We investigate the influence of the choice of the partition of unity on the convergence of the Symmetrized Optimized Restricted Additive Schwarz (SORAS) preconditioner for the reac…
A new perspective on the fictitious space lemma
Xavier Claeys
In the present contribution we propose a new proof of the so-called fictitious space lemma. For the proof, we exhibit an explicit expression for the inverse of additive Schwarz pre…
A Directional Equispaced interpolation-based Fast Multipole Method for oscillatory kernels
Igor Chollet, Xavier Claeys, Pierre Fortin +1
Fast Multipole Methods (FMMs) based on the oscillatory Helmholtz kernel can reduce the cost of solving N-body problems arising from Boundary Integral Equations (BIEs) in acoustic o…
Nonlocal Optimized Schwarz Methods for time-harmonic electromagnetics
Xavier Claeys, Francis Collino, Emile Parolin
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 prese…
Non-self adjoint impedance in Generalized Optimized Schwarz Methods
Xavier Claeys
We present a convergence theory for Optimized Schwarz Methods that rely on a non-local exchange operator and covers the case of coercive possibly non-self-adjoint impedance operato…
Continuity estimates for Riesz potentials on polygonal boundaries
Xavier Claeys, Muhammad Hassan, Benjamin Stamm
Riesz potentials are well known objects of study in the theory of singular integrals that have been the subject of recent, increased interest from the numerical analysis community…
Analysis of the SORAS domain decomposition preconditioner for non-self-adjoint or indefinite problems
Marcella Bonazzoli, Xavier Claeys, Frédéric Nataf +1
We analyze the convergence of the one-level overlapping domain decomposition preconditioner SORAS (Symmetrized Optimized Restricted Additive Schwarz) applied to a generic linear sy…
Local Multiple Traces Formulation for Electromagnetics: Stability and Preconditioning for Smooth Geometries
Alan Ayala, Xavier Claeys, Paul Escapil-Inchauspé +1
We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of t…
Robust treatment of cross points in Optimized Schwarz Methods
Xavier Claeys, Emile Parolin
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…
A new variant of the Optimised Schwarz Method for arbitrary non-overlapping subdomain partitions
Xavier Claeys
We consider a scalar wave propagation in harmonic regime modelled by Helmholtz equation with heterogeneous coefficients. Using the Multi-Trace Formalism (MTF), we propose a new var…
Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner
Lucas Chesnel, Xavier Claeys, Sergei A. Nazarov
We investigate the eigenvalue problem in a 2D domain divided into two regions . We are interested in situations where …
Essential spectrum of local multi-trace boundary integral operators
Xavier Claeys
Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary…
A numerical approach for the Poisson equation in a planar domain with a small inclusion
Lucas Chesnel, Xavier Claeys
We consider the Poisson equation in a domain with a small hole of size . We present a simple numerical method, based on an asymptotic analysis, which allows to approximate robus…
Spectrum of a diffusion operator with coefficient changing sign over a small inclusion
Lucas Chesnel, Xavier Claeys, Sergei A. Nazarov
We study a spectral problem for a diffusion like equation in a 3D domain . The main originality lies in the presence of a parameter , whose sign changes o…
A curious instability phenomenon for a rounded corner in presence of a negative material
Lucas Chesnel, Xavier Claeys, Sergey A. Nazarov
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at op…