A high performance approach for solving the high voltage direct current ion flow field problem by tensor-structured finite element method

In order to achieve high performance for solving the ion flow field problem, an approach is proposed with the tensor-structured finite element method (FEM) to accelerate the Newton iteration. The Poisson equation and the continuity equation are reformulated into the tensor expressions, respectively. The element level evaluation phase is decomposed into the concatenated tensor contraction operations, which is implemented by the highly optimised arithmetic operation provided in Matlab. In contrast to the traditional implemented FEM, the tensor-structured FEM has significantly improved the throughput and achieved high performance. The accuracy and efficiency of the tensor-based algorithm are verified under the unipolar and bipolar model, respectively. The tensor-based algorithm provides one order of magnitude speedup over the traditional algorithm in the elemental evaluation phase. Tensorization' is an efficient way to bridge the algorithm and the hardware.