Lise-Marie Imbert-Gerard

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Scholarly Contributions

Journals/Publications

• Imbert-Gerard, L., Moiola, A., & Stocker, P. (2022). A space–time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients. Mathematics of Computation.
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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 (DG) method for the discretisation of the acoustic wave equation with piecewise-smooth 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 high-order 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 time-harmonic problems with variable coefficients; it turns out that in the case of the time-domain wave equation under consideration the quasi-Trefftz approach allows for polynomial basis functions.
• Sylvand, G., & Imbert-gerard, L. (2021). A roadmap for Generalized Plane Waves and their interpolation properties. Numerische Mathematik, 149(1), 87-137. doi:10.1007/s00211-021-01220-9

Presentations

• Imbert-Gerard, L. (2021). A discussion around the magnetic differential equation. PPPL theory seminar. online: Princeton Plasma Physics Lab.
• Imbert-Gerard, 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.
• Imbert-Gerard, 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.
• Imbert-Gerard, L. (2021). Magnetic coordinates. PPPL Graduate Summer School. online: Princeton Plasma Physics Lab.
• Imbert-Gerard, L. (2021). The Magnetic Differential Equation. PPPL Graduate Summer School. online: Princeton Plasma Physics Lab.
• Imbert-Gerard, L. (2021). Wave propagation in inhomogeneous media: A new family of Generalized Plane Waves. SIAM annual meeting. online: SIAM.
• Imbert-Gerard, 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.
• Imbert-Gerard, L. (2021). Wave propagation in inhomogeneous media: An introduction to quasi-Trefftz methods. numerical analysis and PDE Seminar (Nice). online: University of Nice - Mathematiques.
• Imbert-Gerard, L., & Sylvand, G. (2021). Three quasi-Trefftz bases for the 3D convected Helmholtz equation. European Congress on Computational Methods in Applied Sciences and Engineering. online.
• Imbert-Gerard, L., Paul, E., & Wright, A. (2021). 3D magnetic fields and stellarator design: Challenges and Models. World Congress of Computational Mechanics. online.
• Imbert-Gerard, L., Paul, E., & Wright, A. (2021). An Introduction to Stellarators: a periodic transport equation. SIAM Conference on Computational Science and Engineering. online: SIAM.