Accuracy and efficiency considerations in the solution of extremely large electromagnetics problems

This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems.