A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities

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

Nagoya University, Japan

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© 2021 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).



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.


adjoint problem, boundary element method, tangential derivative of potential, topological derivative, topology optimization


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