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Stable and accurate outgoing wave filters for anisotropic and nonlocal waves. (English) Zbl 1176.65116

Blackmore, Denis (ed.) et al., Frontiers of applied and computational mathematics. Dedicated to Daljit Singh Ahluwalia on his 75th birthday. Papers based on the presentations at the 5th annual frontiers in applied and computational mathematics conference (FACM ’08), Newark, NJ, USA, 19–21 May 2008. Hackensack, NJ: World Scientific (ISBN 978-981-283-528-4/hbk). 240-247 (2008).
Summary: The perfectly matched layer (PML) is currently the mainstay of absorbing boundary conditions. For some anisotropic wave equations the PML is exponentially unstable in time. We present in this work a new method of open boundaries, the phase space filter, which is stable for all wave equation.
Outgoing waves can be are waves located near the boundary of the computational domain with group velocities pointing out. Phase space filtering involves periodically removing only outgoing waves from the solution, leaving non-outgoing waves unchanged. We apply this method to the Euler equations (linearized about a jet flow), Maxwell equations in a birefringent medium and the quasi-geostrophic equations.
For the entire collection see [Zbl 1165.65002].

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L05 Wave equation
35L65 Hyperbolic conservation laws
35Q61 Maxwell equations
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