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DRBEM solution of exterior nonlinear wave problem using FDM and LSM time integrations

机译：使用FDM和LSM时间积分的外部非线性波问题的DRBEM解决方案

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摘要

The nonlinear wave equation is solved numerically in an exterior region. For the discretization of the space derivatives dual reciprocity boundary element method (DRBEM) is applied using the fundamental solution of Laplace equation. The time derivative and the nonlinearity are treated as the nonhomogenity. The boundary integrals coming from the far boundary are eliminated using rational and exponential interpolation functions which have decay properties far away from the region of interest. The resulting system of ordinary differential equations in time are solved using finite difference method (FDM) with a relaxation parameter and least squares method (LSM). The proposed methods are examined with numerical test problems in which the behaviours of solutions are known. Although it gives almost the same accuracy with the DRBEM+FDM procedure, DRBEM + LSM solution procedure is preferred, since it is a direct method without the need of a parameter.
机译：非线性波动方程在外部区域数值求解。为了离散化空间导数，使用拉普拉斯方程的基本解采用了双互易性边界元方法（DRBEM）。时间导数和非线性被视为非均匀性。使用有理和指数插值函数消除了来自远边界的边界积分，这些函数具有远离目标区域的衰减特性。使用带松弛参数的有限差分法（FDM）和最小二乘法（LSM）求解得到的常微分方程组。所提出的方法是通过数值测试问题来检验的，其中解决方案的行为是已知的。尽管它提供与DRBEM + FDM过程几乎相同的精度，但首选DRBEM + LSM解决方案过程，因为它是直接方法，不需要参数。

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