On accuracy of approximate boundary and distributed H1 shape gradient flows for eigenvalue optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:365

Article

Zhu, Shengfeng¹  Hu, Xianliang²  Wu, Qingbiao² 

[1] East China Normal Univ, Sch Math Sci, Shanghai 200241, Peoples R China

[2] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Zhejiang, Peoples R China

关键词: Shape optimization;    Eigenvalue;    Shape gradient flow;    Distributed shape gradient;    Finite element;    Error estimate;   

DOI  :  10.1016/j.cam.2019.112374

来源: Elsevier

【 摘 要 】

The boundary and distributed shape gradients of elliptic eigenvalues in shape optimization are approximated by the finite element method. We show a priori error estimates for the two approximate shape gradients in H-1 shape gradient flows. The convergence analysis shows that the volume integral formula converges faster and offers higher accuracy when the finite element method is used for discretization. Numerical results verify the theory for the Dirichlet case. Shape optimization examples solved by algorithms illustrate the more effectiveness of distributed shape gradients for the Dirichlet case. For optimizing a Neumann eigenvalue, the boundary and volume H-1 flows have the same efficiency. Moreover, we observe that the distributed H-1 shape gradient flow is more efficient than the boundary L-2 shape gradient flow in literature. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

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