Boundary elements with mesh refinements for the wave equation
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39 (4): 867–912 (2018)

The solution of the wave equation in a polyhedral domain admits an asymptotic expansion in a neighborhood of the corners and edges. In this article we formulate boundary and screen problems for the wave equation as an equivalent boundary integral equations in time domain and study the regularity properties and numerical approximation of the solution. Guided by the theory for elliptic equations, graded meshes are shown to recover the optimal approximation rates expected for smooth solutions. Numerical experiments illustrate the theory for screen problems. In particular, we discuss the Dirichlet problem, the Dirichlet-to-Neumann operator and applications to the sound emitted by a tire.
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