34 citations · 105 across the 13 of their papers we have counts for
15 papers
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…
An Introduction to Stellarators: From magnetic fields to symmetries and optimization
Lise-Marie Imbert-Gerard, Elizabeth J. Paul, Adelle M. Wright
In this self-contained document, we aim to present the basic theoretical building blocks to understand modeling of stellarator magnetic fields, some of the challenges associated wi…
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…
Well-posedness and generalized plane waves simulations of a 2D mode conversion model
Lise-Marie Imbert-Gérard
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the pl…
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…