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
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DOI：
10.2495/cmem-v9-n1-74-82
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Peijun Tang;Toshiro Matsumoto;H. Isakari;Toru Takahashi
中科院分区：
文献类型：
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作者：
Peijun Tang;Toshiro Matsumoto;H. Isakari;Toru Takahashi
考虑了二维Helmholtz方程的一个特殊拓扑优化问题，其目标函数为边界势的切向导数。为了导出伴随问题，传统拓扑优化的泛函需要对势及其通量进行边界积分。对于具有切向导数的本目标泛函，将分部积分应用于具有势的变化的切向导数的部分，以生成易于处理的伴随问题。在目标函数的变分中使用了导出的伴随问题，并在常规表达式中导出了拓扑导数。
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.