通用有限元系统实现无限域波动仿真方法

Simulation of wave problem in unbounded domains by commercial FEA software

在有限元模型中加入人工边界,可以进行无限域波动仿真。本文将介绍一种改进的Higdon人工边界,并通过适当的变换形式,将其在通用有限元软件上实现。最后通过数值实验验证了这种方法具有良好的稳定性和计算精度,并且实施简单方便,其他人工边界条件可参照本文方法,通过变换形式在通用有限元程序中实现。

In practical calculation,it is often essential to truncate the unbounded medium in order to render the computational domain finite and apply absorbing boundary conditions at the computational boundary.A new method based on Higdon＇s absorbing boundary（HK ABCs） is introduced,which simplifies the computation procedure of the HK ABCs＇ partial equation by introducing a number of auxiliary variables.Then appropriately transforming the simplified equations to the form that is feasibly applied to commercial finite element code.In the transformation of the FEA discrete equations,the coherent forces which derived from the ABCs is moved to the right of the equation,equated to the boundary forces.In the resultant application,we can use any order of the ABCs in the FEA computation,meanwhile,keep FEA code running stably.Numerical examples are presented to illustrate the effectiveness of the method.Current limitations and possible extensions are also discussed.