LiseMarie ImbertGerard
 Associate Professor, Mathematics
 Member of the Graduate Faculty
Contact
 (520) 6210673
 Mathematics, Rm. 115
 Tucson, AZ 85721
 lmig@arizona.edu
Degrees
 Ph.D.
 Universite Pierre et Marie Curie  Paris 6, Paris, France
 Mathematical and numerical methods for some wave problems in magnetic plasmas.
Work Experience
 University of Maryland, College Park, Maryland (2018  2020)
Awards
 Leslie Fox prize in Numerical Analysis, second prize
 Summer 2017
 Cathleen Morawetz Fellowship
 Courant Institute, Spring 2016
Interests
No activities entered.
Courses
202324 Courses

Thry of Complex Variable
MATH 424 (Spring 2024) 
Math Prin Numeric Anls
MATH 475A (Fall 2023)
202223 Courses

Research
MATH 900 (Spring 2023) 
Calculus II
MATH 129 (Fall 2022) 
Math Prin Numeric Anls
MATH 475A (Fall 2022) 
Research
MATH 900 (Fall 2022)
202122 Courses

Appl Partial Diff Eq
MATH 456 (Spring 2022) 
Intro to Linear Algebra
MATH 313 (Fall 2021)
202021 Courses

Intro to Linear Algebra
MATH 313 (Spring 2021) 
Calculus I
MATH 125 (Fall 2020)
Scholarly Contributions
Journals/Publications
 ImbertGerard, L., Moiola, A., & Stocker, P. (2022). A space–time quasiTrefftz DG method for the wave equation with piecewisesmooth coefficients. Mathematics of Computation.More infoTrefftz methods are highorder 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 piecewiseconstant. We introduce a “quasiTrefftz” discontinuous Galerkin (DG) method for the discretisation of the acoustic wave equation with piecewisesmooth material parameters: the discrete functions are elementwise approximate PDE solutions. We show that the new discretisation enjoys the same excellent approximation properties as the classical Trefftz one, and prove stability and highorder convergence of the DG scheme. We introduce polynomial basis functions for the new discrete spaces and describe a simple algorithm to compute them. The technique we propose is inspired by the generalised plane waves previously developed for timeharmonic problems with variable coefficients; it turns out that in the case of the timedomain wave equation under consideration the quasiTrefftz approach allows for polynomial basis functions.
 Sylvand, G., & Imbertgerard, L. (2021). A roadmap for Generalized Plane Waves and their interpolation properties. Numerische Mathematik, 149(1), 87137. doi:10.1007/s00211021012209
Presentations
 ImbertGerard, L. (2021). A discussion around the magnetic differential equation. PPPL theory seminar. online: Princeton Plasma Physics Lab.
 ImbertGerard, L. (2021). Bits and pieces of an introduction to Stellarator design The Magnetic Differential Equation. INRIA Cage team seminar. online: INRIA Cage team  Laboratoire Jacques Louis Lions  Sorbonne universite.
 ImbertGerard, L. (2021). Bits and pieces of an introduction to Stellarator design The Magnetic Differential Equation. Numerical Methods in Plasma Physics seminar. online: Max Planck Institute for Plasma Physics  Garching.
 ImbertGerard, L. (2021). Magnetic coordinates. PPPL Graduate Summer School. online: Princeton Plasma Physics Lab.
 ImbertGerard, L. (2021). The Magnetic Differential Equation. PPPL Graduate Summer School. online: Princeton Plasma Physics Lab.
 ImbertGerard, L. (2021). Wave propagation in inhomogeneous media: A new family of Generalized Plane Waves. SIAM annual meeting. online: SIAM.
 ImbertGerard, L. (2021). Wave propagation in inhomogeneous media: An introduction to Generalized Plane Waves. Applied Mathematics and Statistics Colloquium. online: Colorado school of Mines  Department of Applied Mathematics and Statistics.
 ImbertGerard, L. (2021). Wave propagation in inhomogeneous media: An introduction to quasiTrefftz methods. numerical analysis and PDE Seminar (Nice). online: University of Nice  Mathematiques.
 ImbertGerard, L., & Sylvand, G. (2021). Three quasiTrefftz bases for the 3D convected Helmholtz equation. European Congress on Computational Methods in Applied Sciences and Engineering. online.
 ImbertGerard, L., Paul, E., & Wright, A. (2021). 3D magnetic fields and stellarator design: Challenges and Models. World Congress of Computational Mechanics. online.
 ImbertGerard, L., Paul, E., & Wright, A. (2021). An Introduction to Stellarators: a periodic transport equation. SIAM Conference on Computational Science and Engineering. online: SIAM.