A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation

Toru Takahashi, Daisuke Sato, Hiroshi Isakari, Toshiro Matsumoto

研究成果: Article査読

4 被引用数 (Scopus)

抄録

This paper presents a shape optimisation system to design the shape of an acoustically-hard object in the three-dimensional open space. The boundary element method (BEM) is suitable to analyse such an exterior field. However, the conventional BEM, which is based on piecewise polynomial shape and approximate (interpolation) functions, can require many design variables because they are usually chosen as a part of the nodes of the underlying boundary element mesh. In addition, it is not easy for the conventional method to compute the gradient of the sound pressure on the surface, which is necessary to compute the shape derivative of our interest, of a given object. To overcome these issues, we employ the isogeometric boundary element method (IGBEM), which was developed in our previous work. With using the IGBEM, we can design the shape of surfaces through control points of the NURBS surfaces of the target object. We integrate the IGBEM with the nonlinear programming software through the adjoint variable method (AVM), where the resulting adjoint boundary value problem can be also solved by the IGBEM with a slight modification. The numerical verification and demonstration validate our shape optimisation framework.

本文言語English
論文番号103126
ジャーナルCAD Computer Aided Design
142
DOI
出版ステータスPublished - 2022 1月
外部発表はい

ASJC Scopus subject areas

  • コンピュータ サイエンスの応用
  • コンピュータ グラフィックスおよびコンピュータ支援設計
  • 産業および生産工学

フィンガープリント

「A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル