A new adjoint problem for two-dimensional helmholtz equation to calculate topological derivatives of the objective functional having tangential derivative quantities

Peijun Tang, Toshiro Matsumoto, Hiroshi Isakari, Toru Takahashi

Research output: Contribution to journalArticlepeer-review

Abstract

A special topology optimization problem is considered whose objective functional consists of tangential derivative of the potential on the boundary for two-dimensional Helmholtz equation. In order to derive the adjoint problem, the functional of the conventional topology optimizations required a boundary integral of the potential and its flux. For the present objective functional having the tangential derivative, integration by parts is applied to the part having the tangential derivative of the variation of the potential to generate a tractable adjoint problem. The derived adjoint problem is used in the variation of the objective function, and the topological derivative is derived in the conventional expression.

Original languageEnglish
Pages (from-to)74-82
Number of pages9
JournalInternational Journal of Computational Methods and Experimental Measurements
Volume9
Issue number1
DOIs
Publication statusPublished - 2020 Mar 4
Externally publishedYes

Keywords

  • Adjoint problem
  • Boundary element method
  • Tangential derivative of potential
  • Topological derivative
  • Topology optimization

ASJC Scopus subject areas

  • Computational Mechanics
  • Modelling and Simulation
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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