Lise-Marie Imbert-Gérard
Book
- An introduction to stellarators: From magnetic fields to symmetries and optimization, (link). LMIG, E. J. PAUL, A. M. WRIGHT. SIAM (2024), DOI 10.1137/1.9781611978223. Freely available here.
Articles and pre-prints
- Quasi-Trefftz spaces for the first-order time-harmonic Maxwell's equation, (arxiv) Ilaria Fontana, LMIG, Submitted.
- Quasi-Trefftz spaces for a second-order time-harmonic Maxwell's equation, (arxiv) Ilaria Fontana, LMIG, Submitted.
- Local Taylor-based quasi-Trefftz spaces for scalar linear equations, (arxiv) LMIG, Submitted.
- Quasi-Trefftz spaces for a first-order formulation of the Helmholtz equation, (arxiv) LMIG, A. LAGARDERE, G. SYLVAND, S. TORDEUX, Submitted.
- A discontinuous Galerkin method for elliptic-hyperbolic equations: the Tricomi problem, (arxiv). C. PERINATI, LMIG, A. MOIOLA, P. STOCKER. Accepted for publication in ESAIM:M2AN (https://doi.org/10.1051/m2an/2026081).
- Generalized Plane Wave quasi-Trefftz spaces for wave propagation in inhomogeneous media, (link) (arxiv). I. FONTANA, LMIG. Proceedings of the 11th Convention of the European Acoustics Association Forum Acusticum / EuroNoise 2025, ISBN: 978-84-87985-35-5. DOI: 10.61782/fa.2025.0967.
- Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems, (link) (arxiv). LMIG, A. MOIOLA, C. PERINATI, P. STOCKER. IMA Journal of Numerical Analysis (2025). DOI: 10.1093/imanum/drae094.
- Three types of quasi-Trefftz functions for the 3D convected Helmholtz equation: construction and approximation properties, (link). LMIG, G. SYLVAND. IMA Journal of Numerical Analysis (2024) DOI: 10.1093/imanum/drae060.
- A space-time quasi-Trefftz DG method for the wave equation with piecewise-smooth coefficients, (link) (arxiv). LMIG, A. MOIOLA, P. STOCKER. Mathematics of Computation (2022).
- Amplitude-based Generalized Plane Waves: new Quasi-Trefftz functions for scalar equations in 2D. (link). LMIG. SIAM Journal Numerical Analysis, 59 (2021) 3, 1663-1686.
- A roadmap for Generalized Plane Waves and their interpolation properties, (link). LMIG, G. SYLVAND. Numerische Mathematik, 149 (2021) 1, 87-137.
- Taylor States in Stellarators: A Fast High-order Boundary Integral Solver, (link). D. MALHOTRA, A. CERFON, LMIG, M. O'NEIL. Journal of Computational Physics, 397 (2019).
- Integral equation methods for electrostatics, acoustics and electromagnetics in smoothly varying, anisotropic media , (link). LMIG, F. VICO, L. GREENGARD, M. FERRANDO. SIAM Journal Numerical Analysis, 57 (2019) 3, 1020–1035.
- Pseudo-spectral methods for the Laplace-Beltrami equation and the Hodge decomposition on surfaces of genus one , (link). LMIG, L. GREENGARD. Numerical Methods for PDEs, 33 (2017) 941–955.
- Numerical simulation of wave propagation in inhomogeneous media using Generalized Plane Waves, (link). LMIG, P. MONK. ESAIM: M2AN, 51 4 (2017) 1387-1406.
- Solutions to the cold plasma model at resonances, (link). B. DESPRES, LMIG, O. LAFITTE. Journal de l'École polytechnique — Mathématiques, 4 (2017), p. 177-222.
- Fast, adaptive, high order accurate discretization of the Lippmann-Schwinger equation in two dimensions, (link). S. AMBIKASARAN, C. BORGES, LMIG, L. GREENGARD. SIAM J. Sci. Comput., 38 3 (2016), A1770–A1787.
- A numerical study of the solution of X-mode equations around a hybrid resonance, (link). C. CALDINI-QUEIROS, B. DESPRES, LMIG, M. KACHANOVSKA, (hal-01114791). CEMRACS'14 – Numerical Modeling of Plasmas, 1-21, ESAIM Proc., 53, 2016.
- Well-posedness and generalized plane waves simulations of a 2D mode conversion model, (link). LMIG. JCP (2015), pp. 105-124.
- Interpolation properties of generalized plane waves, (link). LMIG. Numerische Mathematik 131 (2015) 4, pp.683--711.
- Hybrid resonance of Maxwell's equations in slab geometry, (link). B. DESPRES, LMIG, R. WEDER. Journal de Math. Pures et Appliquées, 101 (2014) 5, pp.623--659.
- A generalized plane wave numerical method for smooth non constant coefficients, (link). LMIG, B. DESPRES. IMA Journal of Numerical Analysis 34 (2014).
- Magnetic Equations with FreeFem++: the Grad-Shafranov Equation & the Current Hole, E. DERIAZ, B. DESPRES, G. FACCANONI, K. P. GOSTAF, LMIG, G. SADAKA et R. SART, CEMRACS'10 research achievements: numerical modeling of fusion, 76-94, ESAIM Proc., 32, EDP Sci., Les Ulis, 2011.
- Conservative numerical methods for a two-temperature resistive MHD model with self-generated magnetic field term, M. WOLFF, S. JAOUEN, LMIG, CEMRACS'10 research achievements: numerical modeling of fusion, 195-210, ESAIM Proc., 32, EDP Sci., Les Ulis, 2011.
- (arxiv links)
Other publications
- Report on the Multi-Fidelity Methods for Fusion Energy IPAM Long Program, Spring 2026. V. Artigues, E. Chirtel, R. Conlin, I.-G. Farcas, G. Geraci, K. Gill, M. Golden, W. Guo, A. Hakim, J. Hittinger, G. K. Holt, L.-M. Imbert-Gérard, UF. Jenko, B. Kramer, G. Merlo, S. Mou, E. Paul, U. Shumlak, P. Travis, G. Vogman, T.-H. Watanabe, T. Wildey, A. Wright, and B. Zhu. Technical report, Sponsoring organization: Institute for Pure and Applied Mathematics, UCLA, DOI: 10.82930/B64W2C.
- Fusion Energy Science 2023 Theory & Simulation Performance Target Report. S. R. Hudson, A. M. Wright, A. S. Ware, J. Schmitt, J. D. Hanson, M. Cianciosa, C. Zhu, A. Guiliani, E. J. Paul, L.-M. Imbert-Gérard, W. Sengupta, R. Jorge, D. Panici, D. Dudt, E. Kolemen, A. Baillod, Z. Qu, N. M. Ferraro, S. Saxena, M. Landreman, Z. Tecchiolli, J. Loizu, F. Hindenlang, R. Koberl. Technical report, Sponsoring organization: USDOE Office of Science - Fusion Energy Sciences, DOI: 10.2172/2458165.
PhD thesis
- Mathematical and numerical analysis of wave problems for magnetic plasmas, link.
Older side-projects
CEMRACS 2010 on numerical models for fusion.
- EMAFF : magnetic equations with FreeFem.
- RESIST : numerical methods for resistive MHD.
French 2011 math-industry weeks :
- With Alain Fuser from GDF Suez, optimization for solar energy production (report).
- With Philippe Saadé from PICVIZ labs, study of high dimensional data.