Mesh quality preserving shape optimization using nonlinear extension operators

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.

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Cited by in corpus (7)

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• A Scalable Algorithm for Shape Optimization with Geometric Constraints in Banach Spaces
• Fluid dynamic shape optimization using self-adapting nonlinear extension operators with multigrid preconditioners
• PDE constrained shape optimisation with first-order and Newton-type methods in the $W^{1,\infty }$ topology
• Exploiting locality in sparse polynomial approximation of parametric elliptic PDEs and application to parameterized domains
• Homotopy methods for higher order shape optimization: A globalized shape-Newton method and Pareto-front tracing
• Shape optimization in $W^{1,\infty }$ with geometric constraints: a study in distributed-memory systems