53 citations · 90 across the 6 of their papers we have counts for
8 papers · 1 filter
Multiscale Methods for wave propagation in materials with sign-changing coefficients
Eric T. Chung, Patrick Ciarlet, Xingguang Jin +1
From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These…
On some coupled local and nonlocal diffusion models
Juan Pablo Borthagaray, Patrick Ciarlet
We study problems in which a local model is coupled with a nonlocal one. We propose two energies: both of them are based on the same classical weighted -semi norm to model the…
Explicit T -coercivity for the Stokes problem: a coercive finite element discretization
Patrick Ciarlet, Erell Jamelot
Using the T-coercivity theory as advocated in [Chesnel, Ciarlet, T -coercivity and continuous Galerkin methods: application to transmission problems with sign changing coefficients…
Multiscale modeling for a class of high-contrast heterogeneous sign-changing problems
Eric T. Chung, Patrick Ciarlet, Xingguang Jin +1
The mathematical formulation of sign-changing problems involves a linear second-order partial differential equation in the divergence form, where the coefficient can assume positiv…
An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients
Patrick Ciarlet, David Lassounon, Mahran Rihani
In this work, we present a new numerical method for solving the scalar transmission problem with sign-changing coefficients. In electromagnetism, such a transmission problem can oc…
On the convergence in -norm for the fractional Laplacian
Juan Pablo Borthagaray, Patrick Ciarlet
We consider the numerical solution of the fractional Laplacian of index in a bounded domain with homogeneous boundary conditions. Its solution a priori belongs to…
Theory and implementation of -matrix based iterative and direct solvers for Helmholtz and elastodynamic oscillatory kernels
Stéphanie Chaillat, Luca Desiderio, Patrick Ciarlet
In this work, we study the accuracy and efficiency of hierarchical matrix (-matrix) based fast methods for solving dense linear systems arising from the discretization…
On the use of Perfectly Matched Layers at corners for scattering problems with sign-changing coefficients
Anne-Sophie Bonnet-Ben Dhia, Camille Carvalho, Lucas Chesnel +1
We investigate in a D setting the scattering of time-harmonic electromagnetic waves by a plasmonic device, represented as a non dissipative bounded and penetrable obstacle with…