Parallel Finite Element Computation of Time-Varying Ionized Field Around Hybrid AC/DC Lines via Fine-Grained Domain Decomposition

The time-varying hybrid ionized field around HVAC and HVDC transmission lines is a computationally demanding problem due to the coupling of the Poisson's equation and current continuity equation, as well as the involvement of large matrix in traditional Galerkin finite element method (FEM). In this paper, a fine-grained nodal domain decomposition (NDD) scheme, which enables each sub-domain with only one unknown to be solved independently in a massively parallel fashion, was employed to solve the Poisson's equation. Meanwhile, an upwind nodal charge conservation (NCC) method is applied to solve the current continuity equation without numerical oscillation at each finite element nodal level. The computation of NDD and NCC can both be vectorized and mapped to massive computational cores and utilize the computing power of graphics processor units (GPUs). The interaction between HVAC and HVDC was solved without the Deutsch's assumption to guarantee the accuracy, and the wind influence can be considered. With the massively parallel NDD scheme and NCC scheme, both the Poisson's equation and the current continuity equation were solved at each time-step on GPUs to obtain the transient details of the hybrid ionized field. The performance of the proposed method is tested and compared with commercial software, showing a speedup of 17 times for an 8184-node finite element case with a mean relative error of 0.07%.