TY - JOUR
T1 - A Shape Optimisation with the Isogeometric Boundary Element Method and Adjoint Variable Method for the Three-Dimensional Helmholtz Equation
AU - Takahashi, Toru
AU - Sato, Daisuke
AU - Isakari, Hiroshi
AU - Matsumoto, Toshiro
N1 - Funding Information:
This work was partially by JSPS KAKENHI, Japan Grant Number 18K11335.This research was supported by JSPS KAKENHI (Grant Number: 18K11335). We would like to thank K. Nakai for helping us to create the NURBS model in Section 4.5. In addition, we would like to thank the anonymous referees for helping us to improve the original manuscript.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2022/1
Y1 - 2022/1
N2 - 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.
AB - 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.
KW - Adjoint variable method
KW - Boundary element method
KW - Isogeometric analysis
KW - Nonlinear programming problem
KW - Shape optimisation
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U2 - 10.1016/j.cad.2021.103126
DO - 10.1016/j.cad.2021.103126
M3 - Article
AN - SCOPUS:85116608790
SN - 0010-4485
VL - 142
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
M1 - 103126
ER -