一种求解电磁场本征值问题的新方法

A NEW METHOD FOR SOLVING ELECTROMAGNETIC EIGENVALUE PROBLEMS

在齐次Helmholtz方程的右端加上一个已知的激励函数，并给未知的本征值赋一个猜值，就得到与原本征值问题对应的定解问题．文中证明当这个猜值趋近正确的本征值时，定解问题解的范数将趋近于无穷大，用这一结论作为判据就可将本征值问题的求解转化为定解问题的求解．这一新方法的主要特点是可以利用解稀疏矩阵方程的算法求解非标准的稀疏矩阵本征方程．

By adding a known source function to the right-hand side and giving the unknown eigenvalue a trial value, the homogeneous Helmholtz equation that models the eigenvalue problems is turned into an inhomogeneous Helmholtz equation that models the deterministic problems. When the trial value approaches one of the correct eigenvalues, the norm of the solution of the deterministic equation will approach infinite. Taking this as a criterion, an eigenvalue problem can be turned into a deterministic problem. The most attractive feature of this method is that it can solve the non - standard eigenvalue sparse matrix equation by using the methods for the deterministic sparse matrix equation.