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Abstract The analysis of electrothermal coupling problems finds extensive application in engineering. However, for large-scale electrothermal coupling problems, the time cost and storage requirements for solving them using the finite element method (FEM) are substantial. We optimize the finite element electrothermal coupling computation from two aspects: computational speed and storage usage. Based on the assembly-free FEM, we explore the symmetry of element matrices to reduce storage for second-order tetrahedral elements and propose a graphics processing unit (GPU) parallel algorithm to improve computational speed. At the same time, we allocate the parallel parts of an electrothermal coupling problem to two GPUs to improve the speed further. In addition, for the three types of boundary conditions in electrothermal coupling problems, we design parallel application methods suitable for assembly-free FEM. Finally, we compare our strategy with methods from other literature through the numerical experiment. Our method reduces the element matrices’ storage by 45%. Compared with the solution process using the element level method and degree of freedom level method, our strategy achieves average acceleration ratios of 5.83 and 1.38, respectively.
Wu et al. (Wed,) studied this question.