Fast Electromagnetic Integral-Equation Solvers on Graphics Processing Units

A survey of electromagnetic integral-equation solvers, implemented on graphics processing units (GPUs), is presented. Several key points for efficient GPU implementations of integral-equation solvers are outlined. Three spatial-interpolation-based algorithms, including the Nonuniform-Grid Interpolation Method (NGIM), the box Adaptive-Integral Method (B-AIM), and the fast periodic interpolation method (FPIM), are described to show the basic principles for optimizing GPU-accelerated fast integral-equation algorithms. It is shown that proper implementations of these algorithms lead to very high computational performance, with GPU-CPU speed-ups in the range of 100-300. Critical points for these accomplishments are (i) a proper arrangement of the data structure, (ii) an “on-the-fly” approach, trading excessive memory usage with increased arithmetic operations and data uniformity, and (iii) efficient utilization of the types of GPU memory. The presented methods and their GPU implementations are geared towards creating efficient electromagnetic integral-equation solvers. They can also find a wide range of applications in a number of other areas of computational physics.