## An optimal high-order non-reflecting finite element scheme for wave scattering problems.(English)Zbl 1007.65093

By the authors’ abstract: A new finite element scheme is proposed for the numerical solution of time-harmonic wave scattering problems in unbounded domains. The infinite domain is truncated via an artificial boundary $${\mathcal B}$$ which encloses a finite computational domain $$\Omega$$. On $${\mathcal B}$$ a local high-order non-reflecting boundary condition (NRBC) is applied which is constructed to be optimal in a certain sense. This NRBC involves no high-order derivatives regardless of its order. The order of the scheme may be arbitrarily high. The performance of the method is demonstrated via numerical examples. The method is shown to be highly accurate and stable, and to lead to a well-conditioned matrix problem.

### MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35Q60 PDEs in connection with optics and electromagnetic theory 78A45 Diffraction, scattering 65N15 Error bounds for boundary value problems involving PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 78A40 Waves and radiation in optics and electromagnetic theory 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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