Abstract: 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.

Key words: electromagnetic eigenvalue problems, sparse matrix, numerical methods