The strip method for shape derivatives

Hardesty, Sean; Antil, Harbir; Kouri, Drew P.; Ridzal, Denis

doi:10.1002/nme.6908

The strip method for shape derivatives

Journal Article · Sat Jan 22 23:00:00 EST 2022 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.6908· OSTI ID:1996595

^[1]; Antil, Harbir ^[2]; Kouri, Drew P. ^[3]; Ridzal, Denis ^[3]

Computational Solid Mechanics and Structural Dynamics Sandia National Laboratories Albuquerque New Mexico USA
Department of Mathematical Sciences and the Center for Mathematics and Artificial Intelligence (CMAI) George Mason University Fairfax Virginia USA
Optimization and Uncertainty Quantification Sandia National Laboratories Albuquerque New Mexico USA

Abstract

A major challenge in shape optimization is the coupling of finite element method (FEM) codes in a way that facilitates efficient computation of shape derivatives. This is particularly difficult with multiphysics problems involving legacy codes, where the costs of implementing and maintaining shape derivative capabilities are prohibitive. The volume and boundary methods are two approaches to computing shape derivatives. Each has a major drawback: the boundary method is less accurate, while the volume method is more invasive to the FEM code. We introduce the strip method , which computes shape derivatives on a strip adjacent to the boundary. The strip method makes code coupling simple. Like the boundary method, it queries the state and adjoint solutions at quadrature nodes, but requires no knowledge of the FEM code implementations. At the same time, it exhibits the higher accuracy of the volume method. As an added benefit, its computational complexity is comparable to that of the boundary method, that is, it is faster than the volume method. We illustrate the benefits of the strip method with numerical examples.

View Accepted Manuscript (Publisher)

Sponsoring Organization:: USDOE

OSTI ID:: 1996595

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 7 Vol. 123; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

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