二维散射问题的有限元/边界元方程组求解

Solution of Coupled FEM/BEM Matrix Equation for Two Dimensional Scattering Problem

应用有限元／边界元混合方法计算复杂结构的二维散射问题。有限元处理虚拟边界内部区域，边界元引入辐射条件。采用内视法求解有限元／边界元方程组，减轻了边界元满阵带来的不利影响。文中给出了一般情况下ＴＥ、ＴＭ 波的求解公式，算例结果与公开文献一致。

The hybrid FEM/BEM (Finite Element Method/Boundary Element Method) can be used to solve the electromagnetic scattering problem with considerable precision while keeping the number of nodes to minimum. But the coupled FEM/BEM matrix is no longer sparse and symmetric, thus greatly increasing the computation cost. We adopt the inward looking approach to overcome this shortcoming. We derived the FEM matrix equation (eq.19) which is sparse and symmetric. Instead of coupling eq.(19) with BEM matrix equation (eq.4), we first solve eq.(19) separately and get eq.(20). Then, we couple eq.(20) with eq.(4) to get the coupled FEM/BEM matrix equation (eq.21), which is much easier to solve than the original coupled matrix equation. Computation results obtained by our method (Figs.2 through 4) are in good agreement with previously published data.