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Analyzing three-dimensional transient heat conduction problems with the dimension splitting reproducing kernel particle method

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ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS 2020年 121卷 180-191页

作者： Peng, P. P. Cheng, Y. M. Shanghai Univ Sch Mech & Engn Sci Shanghai Inst Appl Math & Mech Shanghai Key Lab Mech Energy Engn Shanghai 200072 Peoples R China

In this paper, to improve the computational speed of the reproducing kernel particle method (RKPM), the dimension splitting reproducing kernel particle method (DSRKPM) is presented for solving three-dimensional (3D) transient heat conduction problems. The idea of the proposed method is transforming the 3D problem into a series of two-dimensional (2D) ones by using the finite difference method in the splitting direction. Since the shape function of the RKPM for 2D problem is much simpler than the one of 3D problem, the DSRKPM has higher computational speed than the RKPM. To demonstrate the applicability of the proposed method, four example problems are presented, and each of them is solved by the DSRKPM and the RKPM, respectively. And the numerical solutions show that the DSRKPM not only greatly improves the computational efficiency, but also has a higher computational accuracy.

关键词： reproducing kernel particle method dimension splitting method dimension splitting reproducing kernel particle method Finite difference method Transient heat conduction problems

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The dimension splitting reproducing kernel particle method for three-dimensional potential problems

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INTERNATIONAL JOURNAL FOR NUMERICAL methodS IN ENGINEERING 2020年第1期121卷 146-164页

作者： Peng, P. P. Wu, Q. Cheng, Y. M. Shanghai Univ Sch Mech & Engn Sci Shanghai Inst Appl Math & Mech Shanghai Key Lab Mech Energy Engn Shanghai Peoples R China

In this paper, the dimension splitting reproducing kernel particle method (DSRKPM) for three-dimensional (3D) potential problems is presented. In the DSRKPM, a 3D potential problem can be transformed into a series of two-dimensional (2D) ones in the dimension splitting direction. The reproducing kernel particle method (RKPM) is used to solve each 2D problem, the essential boundary conditions are imposed by penalty method, and the discretized equation is obtained from Galerkin weak form of potential problems. Finite difference method is used in the dimension splitting direction. Then, by combining a series of the equations of the RKPM for solving 2D problems, the final equation of the DSRKPM for 3D potential problems is obtained. Five example problems on regular or irregular domains are selected to show that the DSRKPM has higher computational efficiency than the RKPM and the improved element-free Galerkin method for 3D potential problems.

关键词： dimension splitting method dimension splitting reproducing kernel particle method finite difference method potential problem reproducing kernel particle method

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