Scholarlink

<p>Shape and topology optimization constrained by a diffusion equation is modeled by a phase field method. Stabilized gradient flow schemes are proposed to solve the optimal control problems. By addressing the difficulty associated with extra adjoint variables, we derive the unconditional energy stability for the gradient flow using the backward Euler scheme. Moreover, the conditional energy stability of the gradient flow scheme in modified energy using a second-order backward difference formula is demonstrated. Numerical experiments for heat compliance, mean temperature control, and geometric inverse problem are presented to verify the effectiveness of the proposed methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Stabilized gradient flow schemes of phase field model for shape and topology optimization in diffusion

  • 期刊论文

  • 发表日期：

    2026年4月24日

查看全文
  • Jiajie Li,
  • Hui Yang,
  • Shengfeng Zhu

摘要

Shape and topology optimization constrained by a diffusion equation is modeled by a phase field method. Stabilized gradient flow schemes are proposed to solve the optimal control problems. By addressing the difficulty associated with extra adjoint variables, we derive the unconditional energy stability for the gradient flow using the backward Euler scheme. Moreover, the conditional energy stability of the gradient flow scheme in modified energy using a second-order backward difference formula is demonstrated. Numerical experiments for heat compliance, mean temperature control, and geometric inverse problem are presented to verify the effectiveness of the proposed methods.