At the heart of such applications is a solver, which solves a symmetric indefinite dense linear system of size N assembled from the model of the electrical device.
The main computational challenges lie in the solver stage, where an O(N*N*N) computation is required for the direct solution of the linear system about a central frequency omega_c. For the direct solution we use a general symmetric matrix factorization algorithm, requiring N*N*N/3 + O(N*N) FLOPs. This algorithm's efficiency is demonstrated by its parallel speedup of 5 for moderate sized matrices on an 8 node AP3000.
Some of this cost can be amortized using a frequency stepping method , where the system can be solved for nearby frequencies omega by O(N*N) iterative methods, using the solution at omega_c as a preconditioner.
Due to the high parallel efficiency of the direct method, the frequency stepping method reduced parallel solution time by a factor of 2 for moderate-sized matrices, with larger improvements expected for large matrics.