Time exponential splitting integrator for the Klein-Gordon equation with free parameters in the Hagstrom-Warburton absorbing boundary conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:333

Article

Alonso-Mallo, I.¹  Portillo, A. M.² 

[1] Univ Valladolid, Fac Ciencias, Dept Matemat Aplicada, IMUVA, Valladolid, Spain

[2] Univ Valladolid, Escuela Ingn Ind, Dept Matemat Aplicada, IMUVA, Valladolid, Spain

关键词: Splitting methods;    Absorbing boundary conditions;    Dispersive waves;    Auxiliary variables;    Artificial boundary;    Finite differences;   

DOI  :  10.1016/j.cam.2017.10.038

来源: Elsevier

【 摘 要 】

The Klein-Gordon equation on an infinite two dimensional strip is considered. Numerical computation is reduced to a finite domain by using the Hagstrom-Warburton (H-W) absorbing boundary conditions (ABCs) with free parameters in the formulation of the auxiliary variables. The spatial discretization is achieved by using fourth order finite differences and the time integration is made by means of an efficient and easy to implement fourth order exponential splitting scheme which was used in Alonso-Mallo and Portillo (2016) considering the fixed Fade parameters in the formulation of the ABCs. Here, we generalize the splitting time technique to other choices of the parameters. To check the time integrator we consider, on one hand, four types of fixed parameters, the Newmann's parameters, the Chebyshev's parameters, the Fade's parameters and optimal parameters proposed in Hagstrom et al. (2007) and, on the other hand, an adaptive scheme for the dynamic control of the order of absorption and the parameters. We study the efficiency of the splitting scheme by comparing with the fourth-order four-stage Runge-Kutta method. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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