Lise-Marie Imbert-Gérard

University of Arizona

PhysicsDiagonalMathematical analysisResonance (particle physics)SingularityPiecewiseInterpolationAmplitudeHelmholtz equationIntegral equationSolverContext (language use)Applied mathematicsMathematicsPlane waveComputer scienceWave propagationNumerical analysisBasis functionMaxwell's equationsWave equationConvergence (routing)DiscretizationClassical mechanicsOperator (computer programming)Discontinuous Galerkin methodPartial differential equationHermitian matrix

28Publications

7H-index

175Citations

Publications 24

Amplitude-based Generalized Plane Waves: New Quasi-Trefftz Functions for Scalar Equations in two dimensions

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 satisfy the Trefftz pro...

#1Lise-Marie Imbert-GérardH-Index: 7

#2Andrea MoiolaH-Index: 15

Last. Paul StockerH-Index: 1

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Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise constant. We introduce a 'quasi-Trefftz' discontinuous Galerkin method for the discretisation of the acoustic wave equation with piecewise-smooth wavespeed: the discrete functions are elementwise approximate PDE solutions. We show that the new discretisation enjoys the same excellent ...

#1Lise-Marie Imbert-Gérard (UA: University of Arizona)H-Index: 7

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 satisfy the Trefftz property, i.e. they are not exact solutions to the governing equation, they instead satisfy a quasi-Trefftz property: they are only approximate solutions. They lead to high order numerical methods, and this quasi-Trefftz property is critical for their numerical analysis. The present work introduces a new ...

#1Dhairya Malhotra (CIMS: Courant Institute of Mathematical Sciences)H-Index: 8

#2Antoine J. Cerfon (CIMS: Courant Institute of Mathematical Sciences)H-Index: 12

Last. Michael O'Neil (CIMS: Courant Institute of Mathematical Sciences)H-Index: 14

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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 these geometries is a key element for the calculation of stepped pressure stellarator equilibria. The integral representation of the magnetic field in this work is based on the generalized Debye source formulation, and results in a well-conditioned second-kind boundary integral equation. The integral equation solver i...

#1Lise-Marie Imbert-GérardH-Index: 7

#2Elizabeth PaulH-Index: 7

Last. Adelle M. WrightH-Index: 2

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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 with modeling, and optimization for designing stellarators. As often as possible, the ideas will be presented using equations and pictures, and references to other relevant introductory material will be included. This document is accessible to those who may not have a physics background but are interested in applications...

#1Lise-Marie Imbert-GérardH-Index: 7

#2Elizabeth PaulH-Index: 7

Last. Adelle M. WrightH-Index: 2

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The field of plasma physics is broad, with applications in astrophysical and solar phenomena, laser experiments, electronics, and nuclear fusion. Rather than provide a comprehensive introduction to plasma physics, the goal of this document is to explain several important concepts for magnetic confinement in a stellarator. Specifically, we aim to provide the requisite background material in order to discuss challenges related to stellarator equilibrium models, as well as quasisymmetry. Both of th...

#1Lise-Marie Imbert-GérardH-Index: 7

#2Guillaume SylvandH-Index: 1

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 problems with variable coefficients. To tackle problems with constant coefficients, wave-based methods have been widely studied in the literature: they rely on the concept of Trefftz functions, i.e. local solutions to the governing PDE, using oscillating basis functions rather than polynomial functions to represent the nume...

Integral Equation Methods for Electrostatics, Acoustics, and Electromagnetics in Smoothly Varying, Anisotropic Media

#1Lise-Marie Imbert-Gérard (UMD: University of Maryland, College Park)H-Index: 7

#2Felipe Vico (Polytechnic University of Valencia)H-Index: 8

Last. Miguel Ferrando (Polytechnic University of Valencia)H-Index: 9

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We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic, or electromagnetic scattering problems involving anisotropic, inhomogeneous media....

Pseudo‐Spectral Methods for the Laplace‐Beltrami Equation and the Hodge Decomposition on Surfaces of Genus One

#1Lise-Marie Imbert-Gérard (CIMS: Courant Institute of Mathematical Sciences)H-Index: 7

#2Leslie Greengard (CIMS: Courant Institute of Mathematical Sciences)H-Index: 56

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 areas of science, from computer graphics to machine learning to com- putational physics. Here, we present a high-order accurate pseudo-spectral approach, applicable to closed surfaces of genus one in three dimensional space, with a view toward applications in plasma physics and fluid dynamics.

#1Bruno DesprésH-Index: 22

#2Lise-Marie Imbert-Gérard (CIMS: Courant Institute of Mathematical Sciences)H-Index: 7

Last. Olivier LafitteH-Index: 1

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Little is known on the mathematical theory of hybrid and cyclotron solutions of the Maxwell equations with the cold plasma dielectric tensor. Such equations arise in magnetic plasmas such the ones needed for the modeling the an electromagnetic wave in Tokamaks. The behavior of solutions can be extremely different to those in vacuum. This work intends to contribute to the local theory by means of original representation formulas based on special functions and a certain eikonal equation, and with ...

Close Researchers

Bruno Després

H-index : 22

Ricardo Weder

H-index : 24

Guillaume Sylvand

H-index : 1

A. M. Wright

H-index : 3

Elizabeth Paul

H-index : 7

Guillaume Sylvand

H-index : 1

Olivier Lafitte

H-index : 1

Leslie Greengard

H-index : 56

Miguel Ferrando

H-index : 9

Peter Monk

H-index : 56

Carlos F. Borges

H-index : 10

Felipe Vico

H-index : 8

Sivaram Ambikasaran

H-index : 14

Kirill Pichon Gostaf

H-index : 3

Antoine J. Cerfon

H-index : 12