PACM Special Colloquium: Lise-Marie Imbert-Gérard, University of Maryland

Wed, Feb 19, 2020, 11:00 am

Wave propagation in inhomogeneous media: An introduction to Generalized Plane Waves

Trefftz methods rely, in broad terms, on the idea of approximating solutions to Partial Differential Equation (PDEs) using basis functions which are exact solutions of the PDE, making explicit use of information about the ambient medium. But wave propagation problems in inhomogeneous media is modeled by PDEs with variable coefficients, and in general, no exact solutions are available. Generalized Plane Waves (GPWs) are functions that have been introduced, in the case of the Helmholtz equation with variable coefficients, to address this problem: they are not exact solutions to the PDE but are instead constructed locally as high order approximate solutions. We will discuss the origin, the construction, and the properties of GPWs. The construction process introduces a consistency error, requiring a specific analysis.

Lise-Marie graduated from Ecole Normale Superieure de Cachan in 2010. She received her Ph.D. from Universite Pierre et Marie Curie - Paris 6, her thesis advisor was Bruno Despres. She spent a few post-doctoral years at the Courant Institute before joining the University of Maryland in 2018.

Robertson Hall, 001
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