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A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems. (English) Zbl 1004.65098

The paper presents a numerical method for solving nonlinear wave equations in an exterior domain. The method is based on a domain decomposition into a bounded computational domain and an unbounded residual domain using natural boundary reduction to eliminate spurious reflection of waves at the artifical boundaries. After discretizing the equation in time an elliptic problem is solved at each time step with a finite element method using an iterative Schwarz alternating scheme. The convergence rate of the algorithm is discussed and numerical results for a nonlinear wave equation illustrate the accuracy and efficiency of the numerical scheme.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65H10 Numerical computation of solutions to systems of equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
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