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Acadlore takes over the publication of IJCMEM from 2025 Vol. 13, No. 3. The preceding volumes were published under a CC BY 4.0 license by the previous owner, and displayed here as agreed between Acadlore and the previous owner. ✯ : This issue/volume is not published by Acadlore.

Open Access
Research article

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
International Journal of Computational Methods and Experimental Measurements
|
Volume 9, Issue 1, 2021
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Pages 74-82
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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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.

Keywords: adjoint problem, boundary element method, tangential derivative of potential, topological derivative, topology optimization
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GB-T-7714-2015
Tang, P. J., Matsumoto, T., Isakari, H., & Takahashi, T. (2021). A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities. Int. J. Comput. Methods Exp. Meas., 9(1), 74-82. https://doi.org/10.2495/CMEM-V9-N1-74-82
P. J. Tang, T. Matsumoto, H. Isakari, and T. Takahashi, "A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities," Int. J. Comput. Methods Exp. Meas., vol. 9, no. 1, pp. 74-82, 2021. https://doi.org/10.2495/CMEM-V9-N1-74-82
@research-article{Tang2021ANA,
title={A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities},
author={Peijun Tang and Toshiro Matsumoto and Hiroshi Isakari and Toru Takahashi},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2021},
page={74-82},
doi={https://doi.org/10.2495/CMEM-V9-N1-74-82}
}
Peijun Tang, et al. "A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities." International Journal of Computational Methods and Experimental Measurements, v 9, pp 74-82. doi: https://doi.org/10.2495/CMEM-V9-N1-74-82
Peijun Tang, Toshiro Matsumoto, Hiroshi Isakari and Toru Takahashi. "A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities." International Journal of Computational Methods and Experimental Measurements, 9, (2021): 74-82. doi: https://doi.org/10.2495/CMEM-V9-N1-74-82
TANG P J， MATSUMOTO T， ISAKARI H， et al. A New Adjoint Problem for Two-Dimensional Helmholtz Equation to Calculate Topological Derivatives of the Objective Functional Having Tangential Derivative Quantities[J]. International Journal of Computational Methods and Experimental Measurements， 2021， 9(1)： 74-82. https://doi.org/10.2495/CMEM-V9-N1-74-82