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

Special Colloquium

Wave propagation in inhomogeneous media: An introduction to Generalized Plane Waves
Series: Special Colloquium
Location: MATH 501
Presenter: Lise-Marie Imbert-Gerard, University of Maryland

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.

(Refreshments will be served in the Math Commons Room at 3:30 PM)