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Publications in Scientific Journals:

K. Sturm, P. Baumann:
"Adjoint-based methods to compute higher-order topological derivatives with an application to elasticity";
Engineering Computations, ahead-of-print no (2021).



English abstract:
Purpose - The goal of this paper is to give a comprehensive and short review on how to compute the first- and second-order topological derivatives and potentially higher-order topological derivatives for partial differential equation (PDE) constrained shape functionals.
Design/methodology/approach - The authors employ the adjoint and averaged adjoint variable within the Lagrangian framework and compare three different adjoint-based methods to compute higher-order
topological derivatives. To illustrate the methodology proposed in this paper, the authors then apply the methods to a linear elasticity model.
Findings - The authors compute the first- and second-order topological derivatives of the linear elasticity model for various shape functionals in dimension two and three using Amstutzī method, the averaged adjoint method and Delfourīs method.
Originality/value - In contrast to other contributions regarding this subject, the authors not only compute the first- and second-order topological derivatives, but additionally give some insight on various methods and compare their applicability and efficiency with respect to the underlying problem formulation.

Keywords:
Topological derivative, Topology optimisation, Elasticity


"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1108/EC-07-2021-0407


Created from the Publication Database of the Vienna University of Technology.