Boundary element based multiresolution shape optimisation in electrostatics
We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used...
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| Published in | Journal of computational physics Vol. 297; pp. 584 - 598 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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15.09.2015
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| Abstract | We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach. |
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| AbstractList | We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution subdivision surfaces. The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis. The primal and adjoint problems are discretised with the boundary element method using a sufficiently fine control mesh. For shape optimisation the geometry is updated starting from the coarsest control mesh with increasingly finer control meshes. The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes. Moreover, there is no need for mesh regeneration or smoothing during the optimisation due to the absence of a volume mesh. We present several numerical experiments and one industrial application to demonstrate the robustness and versatility of the developed approach. |
| Author | Bandara, Kosala Steinbach, Olaf Cirak, Fehmi Zapletal, Jan Of, Günther |
| Author_xml | – sequence: 1 givenname: Kosala surname: Bandara fullname: Bandara, Kosala email: kkmb2@cam.ac.uk organization: Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1 PZ, United Kingdom – sequence: 2 givenname: Fehmi surname: Cirak fullname: Cirak, Fehmi email: f.cirak@eng.cam.ac.uk organization: Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1 PZ, United Kingdom – sequence: 3 givenname: Günther surname: Of fullname: Of, Günther email: of@tugraz.at organization: Institute of Computational Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria – sequence: 4 givenname: Olaf surname: Steinbach fullname: Steinbach, Olaf email: o.steinbach@tugraz.at organization: Institute of Computational Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria – sequence: 5 givenname: Jan surname: Zapletal fullname: Zapletal, Jan email: jan.zapletal@vsb.cz organization: Department of Applied Mathematics, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba, Czech Republic |
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| Keywords | Shape optimisation Shape derivative Subdivision surfaces Boundary element method Multiresolution analysis |
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| Snippet | We consider the shape optimisation of high-voltage devices subject to electrostatic field equations by combining fast boundary elements with multiresolution... |
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| SubjectTerms | Boundary element method Electrostatic fields Mathematical analysis Multiresolution analysis Optimization Oscillations Robustness Shape derivative Shape optimisation Smoothing Subdivision surfaces Subdivisions |
| Title | Boundary element based multiresolution shape optimisation in electrostatics |
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