GPU Acceleration of a Non-Standard Finite Element Mesh Truncation Technique for Electromagnetics

Abstract

The emergence of General Purpose Graphics Processing Units (GPGPUs) provides new opportunities to accelerate applications involving a large number of regular computations. However, properly leveraging the computational resources of graphical processors is a very challenging task. In this paper, we use this kind of device to parallelize FE-IIEE (Finite Element-Iterative Integral Equation Evaluation), a non-standard finite element mesh truncation technique introduced by two of the authors. This application is computationally very demanding due to the amount, size and complexity of the data involved in the procedure. Besides, an efficient implementation becomes even more difficult if the parallelization has to maintain the complex workflow of the original code. The proposed implementation using CUDA applies different optimization techniques to improve performance. These include leveraging the fastest memories of the GPU and increasing the granularity of the computations to reduce the impact of memory access. We have applied our parallel algorithm to two real radiation and scattering problems demonstrating speedups higher than 140 on a state-of-the-art GPU.

Strategies to parallelize a finite element mesh truncation technique on multi- and manycore architectures

“…As we increase both parameters, the spatial cost of the algorithm also increases, and we exhaust the resources available in the GPU. As we pointed out in [14], the main factor that limits the performance of this parallel algorithm is the number of registers available in each streaming multiprocessor. The computations involved by each iteration of the loop on S involve the use of a very large number of small vectors and scalar variables local to every CUDA thread, which use up even the large number of registers available on most modern GPUs.…”

“…The algorithm cuda S, introduced in [14], is based on a kernel that implements all computations involved in each iteration of the loop on S. The algorithm tries to optimise the management of the different kinds of GPU memory by leveraging the register file and the shared memory of the GPU. Specifically, we copy the elements of vector currents to the shared memory of each block of threads in order to reduce the number of accesses to global memory.…”