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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| Veröffentlicht in: | Journal of computational physics Jg. 517; S. 113347 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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15.11.2024
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| ISSN: | 0021-9991, 1090-2716 |
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| 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.
•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. |
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| AbstractList | 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. 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. |
| ArticleNumber | 113347 |
| Author | Stiernström, Vidar Eriksson, Gustav |
| Author_xml | – sequence: 1 givenname: Gustav orcidid: 0000-0003-4426-3745 surname: Eriksson fullname: Eriksson, Gustav email: gustav.eriksson@it.uu.se – sequence: 2 givenname: Vidar surname: Stiernström fullname: Stiernström, Vidar email: cstierns@stanford.edu |
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| Keywords | Adjoint method Acoustic wave equation Finite differences Summation-by-parts Shape optimization |
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| SubjectTerms | 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 |
| Title | Acoustic shape optimization using energy stable curvilinear finite differences |
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