Acoustic shape optimization using energy stable curvilinear finite differences

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 thr...

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Bibliographic Details
Published in:Journal of computational physics Vol. 517; p. 113347
Main Authors: Eriksson, Gustav, Stiernström, Vidar
Format: Journal Article
Language:English
Published: Elsevier Inc 15.11.2024
Subjects:
Acoustic wave equation
Adjoint method
Beräkningsvetenskap med inriktning mot numerisk analys
Finite differences
Scientific Computing with specialization in Numerical Analysis
Shape optimization
Summation-by-parts
Adjoint method
Acoustic wave equation
Finite differences
Summation-by-parts
Shape optimization
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary: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. •Shape optimization problem constrained by the acoustic wave equation.•Gradient based optimization using the adjoint state framework.•High-order accurate, energy stable, finite difference discretization method.•A new hybrid combination of a weak method (SAT) and a strong method (projection) to impose interface conditions.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2024.113347