25th Annual GAMM-Seminar Leipzig on

FEM and BEM for time-dependent wave problems

Plane Wave Expansions, Optimal Local Radiation Boundary Conditions, and Propagation Algorithms

Thomas Hagstrom (Southern Methodist University)

We discuss the representation of solutions of hyperbolic systems in the time-domain using translating exact or approximate solutions: plane waves, curvelets, and what we call complete plane waves. The latter are half-space representations which both propagate and decay. We show that they lead to highly efficient local radiation boundary condition sequences satisfying optimal complexity estimates. Precisely, an auxiliary variable formulation with O(\ln\frac{1}{\epsilon} \lv \frac{cT}{\delta} degrees-of-freedom per boundary point suffices to achieve an error less than epsilon up to time T assuming sources are separated by delta from the artificial boundary. We also consider the direct use of all three expansions in algorithms to propagate waves to remote locations.

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