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Chebyshev pseudospectral method for wave equation with absorbing boundary conditions that does not use a first order hyperbolic system

机译:不使用一阶双曲系统的具有吸收边界条件的波动方程的Chebyshev伪谱方法

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The analysis and solution of wave equations with absorbing boundary conditions by using a related first order hyperbolic system has become increasingly popular in recent years. At variance with several methods which rely on this transformation, we propose an alternative method in which such hyperbolic system is not used. The method consists of approximation of spatial derivatives by the Chebyshev pseudospectral collocation method coupled with integration in time by the Runge-Kutta method. Stability limits on the timestep for arbitrary speed are calculated and verified numerically. Furthermore, theoretical properties of two methods by Jackiewicz and Renaut are derived, including, in particular, a result that corrects some conclusions of these authors. Numerical results that verify the theory and illustrate the effectiveness of the proposed approach are reported.
机译:近年来,利用相关的一阶双曲系统对具有吸收边界条件的波动方程进行分析和求解变得越来越流行。与依赖此变换的几种方法有所不同,我们提出了一种不使用这种双曲系统的替代方法。该方法包括通过Chebyshev伪谱搭配方法逼近空间导数,再通过Runge-Kutta方法进行时间积分。对任意速度的时间步长的稳定性极限进行了计算和数值验证。此外,还推导了Jackiewicz和Renaut的两种方法的理论特性,特别是纠正了这些作者的某些结论的结果。数值结果验证了该理论并说明了该方法的有效性。

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