Analysis of Fluids and Related Topics: Wave propagation in inhomogeneous media: An introduction to Generalized Plane WavesBA, Lise-Marie Imbert-Gérard, University of Maryland

Thu, Nov 14, 2019, 4:30 pm

Speaker:  Lise-Marie Imbert-Gérard

Abstract:  Trefftz methods rely, in broad terms, on the idea of approximating solutions to PDEs using basis functions which are exact solutions of the Partial Differential Equation (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. 

Fine Hall 322

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