Mesh Quality Preserving Shape Optimization Using Nonlinear Extension Operators

Sofiya Onyshkevych () and Martin Siebenborn ()
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Sofiya Onyshkevych: University Hamburg
Martin Siebenborn: University Hamburg

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 1, No 13, 316 pages

Abstract: Abstract In this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings, we introduce a nonlinear extension operator, which links a boundary control to domain deformations, ensuring admissibility of resulting shapes. The major focus is on comparisons between well-established approaches involving linear-elliptic operators for the extension and the effect of additional nonlinear advection on the set of reachable shapes. It is moreover discussed how the computational complexity of the proposed algorithm can be reduced. The benefit of the nonlinearity in the extension operator is substantiated by several numerical test cases of stationary, incompressible Navier–Stokes flows in 2d and 3d.

Keywords: Aerodynamic shape optimization; Method of mappings; Nonlinear extensions; 35Q93; 49Q10; 35R30; 49K20; 65K10 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01837-8

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