High order full discretizations of coupled wave equations with absorbing boundary conditions and geometric integration

Journal of Computational and Applied Mathematics

2018

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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 [5] considering the fixed Padé 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 Padé's parameters and optimal parameters proposed in [13] 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.

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Section: Time Integrationmentioning

confidence: 99%

“…. , P, φ P +1 = 0, (4) in the vicinity of Γ E . The parameters a j mean cosines of incidence angles and it is natural to take 0 < a j ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

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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

2018

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“…Numerical integrators of arbitrarily high order can be obtained by composition of S [2] [25,27]. For example, in the numerical experiments of Section 5 we have considered the fourth order integrator S [4] S [4] k = S [2] αk • S [2] βk • S [2] αk , with α =…”

Section: Combining the Two Steps And Increasing The Order By Compositionmentioning

confidence: 99%

Time exponential splitting technique for the Klein–Gordon equation with Hagstrom–Warburton high-order absorbing boundary conditions

Journal of Computational Physics

2016

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Klein-Gordon equations on an unbounded domain are considered in one dimensional and two dimensional cases. Numerical computation is reduced to a finite domain by using the Hagstrom-Warburton (H-W) high-order absorbing boundary conditions (ABCs). Time integration is made by means of exponential splitting schemes that are efficient and easy to implement. In this way, it is possible to achieve a negligible error due to the time integration and to study the behavior of the absorption error. Numerical experiments displaying the accuracy of the numerical solution for the two dimensional case are provided. The influence of the dispersion coefficient on the error is also studied.

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Absorbing boundary conditions and geometric integration: A case study for the wave equation

Mathematics and Computers in Simulation

2015