用边界元法求解分片介质中的Helmholtz方程

该文研究了求解分片介质中的Helmholtz方程的边界元法。边界元求解的思路是将分片介质子区域的公共边界当作子区域的外部边界处理 ,在每个子区域采用边界元法 ,再在公共边界上加衔接条件。该文通过大量数值实验 ,并对比边界元法、有限元法、广义差分法求解效果 ,得出边界元法能很好地克服Helmholtz方程解的震荡性 ,采用边界元法求解Helmholtz方程具有稳定性好 ,精度高的优点。

Boundary Element Method for Solving the Helmholtz Equation with Piecewise Medium

How to resolve the Helmholtz equation of piecewise medium is studied by using the boundary element method. The main idea of resolving the boundary element method is that it regards the common boundary of the piecewise medium sub area as the exterior boundary. In every sub area, it uses the boundary element method, and adds some common connective conditions on the common boundary. Based on a great deal of numerical experiments,the effects of resolving the boundary element method, the finite element method and the generalized difference method are contrasted.It is concluded that the boundary element method can overcome the oscillation of the solution of the Helmholtz equation perfectly and has better stability and higher accuracy.