TY - JOUR
T1 - A new adjoint problem for two-dimensional helmholtz equation to calculate topological derivatives of the objective functional having tangential derivative quantities
AU - Tang, Peijun
AU - Matsumoto, Toshiro
AU - Isakari, Hiroshi
AU - Takahashi, Toru
N1 - Funding Information:
ACKNOWLEDGMENT This work was partially supported by the Grant-in-Aid for Scientific Research (A), No. 19H00740, of the Japan Society for the Promotion of Science.
Publisher Copyright:
© 2020 Wit Press. All rights reserved.
PY - 2020/3/4
Y1 - 2020/3/4
N2 - 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.
AB - 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.
KW - Adjoint problem
KW - Boundary element method
KW - Tangential derivative of potential
KW - Topological derivative
KW - Topology optimization
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U2 - 10.2495/CMEM-V9-N1-74-82
DO - 10.2495/CMEM-V9-N1-74-82
M3 - Article
AN - SCOPUS:85102235596
VL - 9
SP - 74
EP - 82
JO - International Journal of Computational Methods and Experimental Measurements
JF - International Journal of Computational Methods and Experimental Measurements
SN - 2046-0546
IS - 1
ER -