Two-Dimensional Shape Optimization with Nearly Conformal Transformations
Abstract
In shape optimization it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy--Riemann equations. Our method allows us to deform meshes in a nearly conformal way and thus approximately preserves the angles of triangles during the optimization process. The performance of our methodology is shown by applying our method to some unconstrained shape functions and a constrained Stokes shape optimization problem.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A3807 - A3830
DOI: 10.1137/17M1152711
ISSN (online): 1095-7197
Copyright
© 2018, Society for Industrial and Applied Mathematics.
History
Submitted: 18 October 2017
Accepted: 4 September 2018
Published online: 20 November 2018
Keywords
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Authors
Funding Information
Engineering and Physical Sciences Research Council https://doi.org/10.13039/501100000266 : EP/L015803/1, EP/K030930/1
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