3 次元音響問題における境界上で定義される目的関数のトポロジー導関数について

抄録

Lately, the topology optimisation has successfully been applied to various problems in engineering such as acoustics, electromagnetics, etc. In a topology optimisation for acoustics, one of the important problems is to design an efficient sound absorbers. In the optimal design for the sound absorbers, it is natural to define the objective functional as sound energy towards the target absorbers. Thus, we sometimes encounter an objective functional defined on a boundary of target objects in the topology optimisation. In this paper, we investigate the topological sensitivity analysis for the objective functional defined on boundary. We prove that, when an energy flux on a boundary is concerned, an additional term is included in the expression of the topological derivative.