34 citations · 105 across the 13 of their papers we have counts for
13 papers · 1 filter
Quasi-Trefftz spaces for the first-order time-harmonic Maxwell's equations
Ilaria Fontana, Lise-Marie Imbert-Gérard
The goal of this article is to study optimal high-order Taylor-based polynomial quasi-Trefftz spaces for first-order time-harmonic Maxwell's equations. Compared with standard polyn…
Waves 2026 Book of Abstracts
Lise-Marie Imbert-Gerard, Chrysoula Tsogka, Daniel Appelo +4
WAVES 2026, 17th International Conference on Mathematical and Numerical Aspects of Wave Propagation Concordia University (John Molson Building), Montreal, Canada, June 22-26, 2026…
Generalized Plane Wave quasi-Trefftz spaces for wave propagation in inhomogeneous media
Ilaria Fontana, Lise-Marie Imbert-Gerard
Partial Differential Equations (PDEs) models for wave propagation in inhomogeneous media are relevant for many applications. We will discuss numerical methods tailored for tackling…
Local Taylor-based polynomial quasi-Trefftz spaces for scalar linear equations
Lise-Marie Imbert-Gerard
Trefftz-type of Galerkin methods for numerical PDEs use discrete spaces of problem-dependent functions. While Trefftz methods leverage discrete spaces of local exact solutions to t…
Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties
Lise-Marie Imbert-Gerard, Guillaume Sylvand
Trefftz methods are numerical methods for the approximation of solutions to boundary and/or initial value problems. They are Galerkin methods with particular test and trial functio…
Amplitude-based Generalized Plane Waves: new Quasi-Trefftz functions for scalar equations in 2D
Lise-Marie Imbert-Gerard
Generalized Plane Waves (GPWs) were introduced to take advantage of Trefftz methods for problems modeled by variable coefficient equations. Despite the fact that GPWs do not satisf…
A roadmap for Generalized Plane Waves and their interpolation properties
Lise-Marie Imbert-Gerard, Guillaume Sylvand
This work focuses on the study of partial differential equation (PDE) based basis function for Discontinuous Galerkin methods to solve numerically wave-related boundary value probl…
Taylor States in Stellarators: A Fast High-order Boundary Integral Solver
Dhairya Malhotra, Antoine Cerfon, Lise-Marie Imbert-Gérard +1
We present a boundary integral equation solver for computing Taylor relaxed states in non-axisymmetric solid and shell-like toroidal geometries. The computation of Taylor states in…
Integral equation methods for electrostatics, acoustics and electromagnetics in smoothly varying, anisotropic media
Lise-Marie Imbert-Gerard, Felipe Vico, Leslie Greengard +1
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inho…
Pseudo-spectral methods for the Laplace-Beltrami equation and the Hodge decomposition on surfaces of genus one
Lise-Marie Imbert-Gerard, Leslie Greengard
The inversion of the Laplace-Beltrami operator and the computation of the Hodge decomposition of a tangential vector field on smooth surfaces arise as computational tasks in many a…
Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves
Lise-Marie Imbert-Gerard, Peter Monk
The Trefftz Discontinuous Galerkin (TDG) method is a technique for approximating the Helmholtz equation (or other linear wave equations) using piecewise defined local solutions of…
Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimension
Sivaram Ambikasaran, Carlos Borges, Lise-Marie Imbert-Gerard +1
We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered fie…
Interpolation properties of generalized plane waves
Lise-Marie Imbert-Gerard
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation prope…