Accuracy: The frequently overlooked parameter in the solution of extremely large problems

We investigate error sources and their effects on the accuracy of solutions of extremely large electromagnetics problems with parallel implementations of the multilevel fast multipole algorithm (MLFMA). Accuracy parameters and their effects on the accuracy of MLFMA solutions are studied for large-scale problems discretized with hundreds of millions of unknowns. We show that some error sources are more dominant and should be suppressed for more accurate solutions; identifying less-effective error sources may allow us to derive more efficient implementations. Based on our analysis, we determine a set of benchmark problems that can be used to compare the accuracy of solvers for large-scale computations. A benchmarking tool is provided at www.cem.bilkent.edu.tr/benchmark.