First and second order unconditionally energy stable schemes for topology optimization based on phase field method

Qian Yu, Kunyang Wang, Binhu Xia and Yibao Li

Applied Mathematics and Computation, 2021, vol. 405, issue C

Abstract: 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.

Keywords: Topology optimization; Phase field method; Second order; Unconditional energy stability (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003568

DOI: 10.1016/j.amc.2021.126267

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