Fast and Accurate Numerical Solution of Allen-Cahn Equation

Kim Yongho; Ryu Gilnam; Choi Yongho

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Fast and Accurate Numerical Solution of Allen-Cahn Equation

机译：Fast and Accurate Numerical Solution of Allen-Cahn Equation

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Simulation speed depends on code structures. Hence, it is crucial how to build a fast algorithm. We solve the Allen-Cahn equation by an explicit finite difference method, so it requires grid calculations implemented by many for-loops in the simulation code. In terms of programming, many for-loops make the simulation speed slow. We propose a model architecture containing a pad and a convolution operation on the Allen-Cahn equation for fast computation while maintaining accuracy. Also, the GPU operation is used to boost up the speed more. In this way, the simulation of other differential equations can be improved. In this paper, various numerical simulations are conducted to confirm that the Allen-Cahn equation follows motion by mean curvature and phase separation in two-dimensional and three-dimensional spaces. Finally, we demonstrate that our algorithm is much faster than an unoptimized code and the CPU operation.

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《Mathematical Problems in Engineering: Theory, Methods and Applications》 |2021年第50期|5263989.1-5263989.12|共12页
作者
Kim Yongho; Ryu Gilnam; Choi Yongho;
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Daegu Univ, Dept IT Convergence Engn, Gyongsan 38453, Gyeongsangbuk D, South Korea;

Daegu Univ, Dept IT Convergence Engn, Gyongsan 38453, Gyeongsangbuk D, South Korea|Daegu Univ, Dept Math & Big Data, Gyongsan 38453, Gyeongsangbuk D, South Korea;

Otto von Guericke Univ, Fac Math, Univ Pl 2, D-39106 Magdeburg, Germany;

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Fast and Accurate Numerical Solution of Allen-Cahn Equation

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