Chapter 19 – Fast Electromagnetic Integral Equation Solvers on Graphics Processing Units

Publisher Summary This chapter presents volumetric and surface integral equation (IE) electromagnetic solvers implemented on graphics processing units (GPUs). It also describes how the nonuniform grid interpolation method (NGIM) and IE solvers can be implemented on GPUs. IE solvers are a powerful tool for the electromagnetic analysis. IEs allow focusing the solution only on the structure of interest, incorporate exact radiation conditions, and do not lead to numerical dispersion. The NGIM, exploits the fact that the field potential far from a source distribution is a function with a known asymptotic behavior. This behavior allows smoothing the fast spatial variations of the potential, computing it on a sparse grid, and interpolating to the required observation points. The algorithm is implemented using a hierarchical domain decomposition method in which the domain is subdivided via an octal tree into a hierarchy of levels comprising subdomains of different sizes. The NGIM divides the computational domain into a hierarchy of boxes containing sources and observers. At any subdivision level, each box is treated as a “parent” box and recursively is divided into eight “child” boxes at lower level. This process stops until boxes at the finest level contain less than a prescribed number of sources. In the implementation of the NGIM, the unique programming mechanisms and hardware arrangement of GPUs are critical to the efficiency of the algorithm. These include the coalesced accessing of the global memory, the utilization of shared memory, and the minimal atomic parallelization unit, “warp.”