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First and second order unconditionally energy stable schemes for topology optimization based on phase field method
Applied Mathematics and Computation ( IF 4 ) Pub Date : 2021-04-17 , DOI: 10.1016/j.amc.2021.126267
Qian Yu , Kunyang Wang , Binhu Xia , Yibao Li

In this paper, we use the phase field method to deal with the compliance minimization problem in topology optimization. A modified Allen-Cahn type equation with two penalty terms is proposed. The equation couples the diffusive interface dynamics and the linear elasticity mechanics. We propose the first- and second-order unconditionally energy stable schemes for the evolution of phase field modeling. The linearly stabilized splitting scheme is applied to improve the stability. The Crank-Nicolson scheme is applied to achieve second-order accuracy in time. We prove the unconditional stabilities of our schemes in analysis. The finite element method and the projected conjugate gradient method combining with fast fourier transform are used to solve the compliance minimization problem. Several experimental results are presented to verify the efficiency and accuracy of the proposed schemes.



中文翻译:

基于相场法的一阶和二阶无条件能量稳定拓扑优化方案

在本文中,我们使用相场方法来处理拓扑优化中的合规性最小化问题。提出了带有两个惩罚项的改进的Allen-Cahn型方程。该方程将扩散界面动力学和线性弹性力学耦合在一起。我们为相场建模的发展提出了一阶和二阶无条件能量稳定方案。应用线性稳定分裂方案以提高稳定性。运用Crank-Nicolson方案在时间上实现了二阶精度。我们证明了我们的方案在分析中的无条件稳定性。有限元法和投影共轭梯度法结合快速傅立叶变换被用来解决最小化依从性的问题。

更新日期:2021-04-18
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