Fast integral equation solvers on Graphics Processing Units for Electromagnetics

This paper presents a comprehensive survey on current status of integral equation solvers implemented on parallel computing systems accelerated by graphics processing units (GPUs) and proposes several key points for efficiently utilizing this type of fundamentally different processors to accelerate several categories of algorithms used by today’s integral equation solvers. Three spatial interpolation-based algorithms, namely Non-uniform Grid Interpolation Method (NGIM), Box-level Adaptive Integral Method (B-AIM) and Fast Periodic Interpolation Method (FPIM) are described in details to show the basic principles for optimizing GPUaccelerated fast algorithms and guide the future designing process of GPU solvers. Due to intrinsic characteristics and careful implementation of these algorithms, speed-ups between 100 and 300 are achieved by a desktop GPU comparing to a desktop CPU at much lower memory consumption. Critical points to these achievements are the brand new programming patterns of GPU applications that trade excessive memory usage and transfer with increased amount of uniformly distributed arithmetic operations. GPU’s unique memory architecture also plays very important roles in deciding the final performance of a GPU code. The presented methods themselves and the designing principles behind them can find very wide applications to many fields inside and outside of computational electromagnetic society.