## High-order non-reflecting boundary scheme for time-dependent waves.(English)Zbl 1025.65049

Summary: A new non-reflecting boundary scheme is proposed for time-dependent wave problems in unbounded domains. The linear time-dependent wave equation, with or without a dispersive term, is considered in a semi-infinite wave guide. The infinite domain is truncated via an artificial boundary $${\mathcal B}$$ , and a high-order non-reflecting boundary condition (NRBC) is imposed on $${\mathcal B}$$. Then the problem is solved numerically in the finite domain bounded by $${\mathcal B}$$.
The new boundary scheme is based on a reformulation of the sequence of NRBCs proposed by R. L. Higdon [SIAM J. Numer. Anal. 31, 64-100 (1994; Zbl 0798.65113)]. In contrast to the original formulation of the Higdon conditions, the scheme constructed here does not involve any high derivatives beyond second order. This is made possible by introducing special auxiliary variables on $${\mathcal B}$$. As a result, the new NRBCs can easily be used up to $$any$$ desired order. They can be incorporated in a finite element or a finite difference scheme; in the present paper the latter is used. The parameters appearing in the NRBC are chosen automatically via a special procedure. Numerical examples concerning a semi-infinite wave guide are used to demonstrate the performance of the new method.

### MSC:

 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35Q53 KdV equations (Korteweg-de Vries equations) 78A50 Antennas, waveguides in optics and electromagnetic theory 78M20 Finite difference methods applied to problems in optics and electromagnetic theory

Zbl 0798.65113
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