Control of bifurcation structures using shape optimization
Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability or bring forward a bifurcation to enable rapid switching between states. We propose a numerical technique for controlling the bifurca...
| Glavni autori: | , , |
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| Format: | Journal article |
| Jezik: | English |
| Izdano: |
Society for Industrial and Applied Mathematics
2022
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| _version_ | 1826278332325429248 |
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| author | Boullé, N Farrell, PE Paganini, A |
| author_facet | Boullé, N Farrell, PE Paganini, A |
| author_sort | Boullé, N |
| collection | OXFORD |
| description | Many problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability or bring forward a bifurcation to enable rapid switching between states. We propose a numerical technique for controlling the bifurcation diagram of a nonlinear partial differential equation by varying the shape of the domain. Specifically, we are able to delay or advance a given branch point to a target parameter value. The algorithm consists of solving a shape optimization problem constrained by an augmented system of equations, the Moore--Spence system, that characterize the location of the branch points. Numerical experiments on the Allen--Cahn, Navier--Stokes, and hyperelasticity equations demonstrate the effectiveness of this technique in a wide range of settings. |
| first_indexed | 2024-03-06T23:42:21Z |
| format | Journal article |
| id | oxford-uuid:6fc16b30-c200-406e-a94f-b17c5fa38fe8 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:42:21Z |
| publishDate | 2022 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:6fc16b30-c200-406e-a94f-b17c5fa38fe82022-03-26T19:32:43ZControl of bifurcation structures using shape optimizationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:6fc16b30-c200-406e-a94f-b17c5fa38fe8EnglishSymplectic ElementsSociety for Industrial and Applied Mathematics2022Boullé, NFarrell, PEPaganini, AMany problems in engineering can be understood as controlling the bifurcation structure of a given device. For example, one may wish to delay the onset of instability or bring forward a bifurcation to enable rapid switching between states. We propose a numerical technique for controlling the bifurcation diagram of a nonlinear partial differential equation by varying the shape of the domain. Specifically, we are able to delay or advance a given branch point to a target parameter value. The algorithm consists of solving a shape optimization problem constrained by an augmented system of equations, the Moore--Spence system, that characterize the location of the branch points. Numerical experiments on the Allen--Cahn, Navier--Stokes, and hyperelasticity equations demonstrate the effectiveness of this technique in a wide range of settings. |
| spellingShingle | Boullé, N Farrell, PE Paganini, A Control of bifurcation structures using shape optimization |
| title | Control of bifurcation structures using shape optimization |
| title_full | Control of bifurcation structures using shape optimization |
| title_fullStr | Control of bifurcation structures using shape optimization |
| title_full_unstemmed | Control of bifurcation structures using shape optimization |
| title_short | Control of bifurcation structures using shape optimization |
| title_sort | control of bifurcation structures using shape optimization |
| work_keys_str_mv | AT boullen controlofbifurcationstructuresusingshapeoptimization AT farrellpe controlofbifurcationstructuresusingshapeoptimization AT paganinia controlofbifurcationstructuresusingshapeoptimization |