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Joint Applied Math and SCCM Seminar
Nonreflecting Boundary Conditions for Multiple Scattering Problems
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The simulation of waves in unbounded media arises in many applications from acoustics, electromagnetics, or elasticity. Standard numerical methods require an artificial boundary, which truncates the unbounded exterior region and restricts the region of interest to a finite computational domain. It then becomes necessary to impose a boundary condition at the artificial boundary, which ensures that the solution inside the computational domain coincides with the originalsolution in the unbounded region. For multiple scattering problems, the use of a single artificial boundary surrounding all scatterers becomes prohibitively expensive. Instead, it is more efficient to embed each scatterer within a separate computational domain. Then, waves that leave a certain sub-domain can enter a different sub-domain at later times; hence waves are no onger purely outgoing in the exterior region, which prohibits the use of many standard pproaches, originally designed for the absorbtion of outgoing waves. Here we show that the Dirichlet-to-Neumann approach for time-harmonic scattering and nonreflecting boundary conditions for time dependent scattering, both essentially exact in the situation of a single computational domain, naturally extend to multiple scattering problems where the computational domain consists of multiple disjoint components. |