Solving bigger problems-by decreasing the operation count and increasing the computation bandwidth

The purpose is to illustrate the computational complexity of modeling large (in wavelengths) electromagnetic problems and to suggest some ways by which the computational requirements can be reduced. The author indicates that, despite the dramatic increase of 106 in throughput that has occurred between the UNIVAC-1 and the current CRAY-2, the impact on the ability to handle computations at ten times the original (temporal) frequency has shown only marginal improvements. This is because the required floating-point operation (FLOP) count for integral-equation (IE) and differential-equation (DE) models grows with frequency. f, as f^x, where 3⩽x⩽9, which means that increasing f by a factor of 10 for a given problem can require from 1000 to 1,000,000,000 more FLOPs. It is suggested that rather than depending on faster computers alone, various analytical and numerical alternatives are needed for reducing the overall FLOP count required to acquire the information desired, some possibilities for which are discussed