Finite-Difference Relaxation for Parallel Computation of Ionized Field of HVDC Lines

Ionized field calculations for high-voltage direct current (HVDC) transmission line is a computationally demanding problem, which can benefit from the application of massively parallel high-performance compute architectures. The finite element method (FEM) commonly employed to solve this problem is both memory and execution time intensive. In this paper, a finite-difference relaxation (FDR) method is proposed to solve a unipolar and a bipolar ionized field problem in an HVDC line. The novel FDR method has several advantages over FEM. First, the scheme is suitable for massively parallel computation and runs much faster: Compared with the commercial FEM software Comsol Multiphysics, the speed-up is more than 14 times in CPU parallelization and 35 times in graphics processor parallel implementation, while providing high accuracy. Moreover, the set of equations in FDR need not be assembled; instead, it is solved by a relaxation scheme and requires much less memory than FEM. Additionally, differentiated grid size with interpolation techniques is proposed to improve the flexibility of FDR for problem domain containing irregular geometries or disproportional sizes.