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Zbl 1004.65098
Du, Q.; Yu, D.
A domain decomposition method based on natural boundary reduction for nonlinear time-dependent exterior wave problems. (English)
[J] Computing 68, No.2, 111-129 (2002). ISSN 0010-485X; ISSN 1436-5057/e

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.
[K.B.Schneider (Berlin)]

MSC 2000:: *65M55 Multigrid methods; domain decomposition (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)
65H10 Systems of nonlinear equations (numerical methods)
65M12 Stability and convergence of numerical methods (IVP of PDE)
35L70 Second order nonlinear hyperbolic equations

Keywords: nonlinear wave equations; exterior domain; domain decomposition; finite element method; iterative Schwarz alternating scheme; convergence; algorithm; numerical results

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Zentralblatt MATH Berlin [Germany]