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.

中文翻译：

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张量结构有限元法求解高压直流离子流场问题的高性能方法

为了实现高性能求解离子流场问题，提出了一种利用张量结构有限元法（FEM）加速牛顿迭代的方法。泊松方程和连续性方程分别重新表述为张量表达式。元素级评估阶段被分解为级联的张量收缩操作，这是通过 Matlab 中提供的高度优化的算术运算来实现的。与传统实现的 FEM 相比，张量结构 FEM 显着提高了吞吐量并实现了高性能。分别在单极和双极模型下验证了基于张量的算法的准确性和效率。基于张量的算法在元素评估阶段比传统算法提供了一个数量级的加速。“张量化”是连接算法和硬件的有效方式。