Work

Acoustic shape optimization using energy stable curvilinear finite differences

Year: 2024

Type: article

Abstract: A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear grids to discretize in space. Representing the design domain through a coordinate mapping from a reference domain, the design shape is obtained by inverting for the discretized coordinate map. The adjoint state framework is employed to efficiently compute the gradient of the loss functional. Using the summation-by-parts properties of the finite difference discretization, we prove stability and dual consistency for the semi-discrete forward and adjoint problems. Numerical experiments verify the accuracy of the finite difference scheme and demonstrate the capabilities of the shape optimization method on two model problems with real-world relevance.

Source: Journal of Computational Physics

DOI: 10.1016/j.jcp.2024.113347

Authors: Gustav Eriksson, Vidar Stiernström

Institution: Uppsala University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,860

Funders: Svenska Forskningsrådet Formas, Vetenskapsrådet, Uppsala Universitet