| Abstract Scope |
The Allen-Cahn equation is widely used to characterize phase separation or the motion of anti-phase boundaries in materials, under the framework of phase field modeling. Its solution is known to be time-consuming when high-resolution meshes and large time scale integration are involved. To overcome this challenge, we propose a convolution tensor decomposition based model reduction method [1] for efficiently solving the Allen-Cahn equation. Numerical examples using both 2D and 3D Allen-Cahn type problems will be presented for demonstrating the performance of the method. The proposed computational framework opens numerous opportunities for simulating complex microstructure formation in materials on large-volume high-resolution meshes at a deeply reduced computational cost.
Reference:
[1] Lu, Ye, Chaoqian Yuan, and Han Guo. "Convolution tensor decomposition for efficient high-resolution solutions to the Allen–Cahn equation." Computer Methods in Applied Mechanics and Engineering (2025). |