GPU-accelerated ADI-PE method for analysis of EM scatterings

The parabolic equation (PE) can be solved in one dimension by using the alternating direction implicit (ADI) scheme. In this way, the reduced scattered fields can be calculated line by line in each transverse plane. Thus both the CPU time and the memory requirement can be largely reduced. In this reported work, the ADI-PE method is adapted to graphics processing units (GPUs) implementation with the CUDA. The processes of both the matrix-filling and the equation-solving can be accelerated by the CUDA-based GPU. A couple of numerical results are given to demonstrate that the speedup of over 87 times can be obtained by the GPU implementation when compared with the CPU one.