Book project

• An introduction to stellarators: From magnetic fields to symmetries and optimization, LMIG, E. J. PAUL, A. M. WRIGHT. SIAM, to appear 2024.

Submitted

• A quasi-Trefftz space for the time-harmonic Maxwell's equation, LMIG, Submitted.
• Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems, (arxiv). LMIG, A. MOIOLA, C. PERINATI, P. STOCKER. Submitted.
• Taylor-based quasi-Trefftz spaces for scalar linear equations, LMIG, Submitted.

Published

• 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)