A level-set topological optimization method to analyze two-dimensional thermal problem using BEM

Jing, Guoxian; Gao, Haifeng; Xiang, Jiawei

doi:10.1016/j.apm.2019.10.002

Cited by 16 publications

(3 citation statements)

References 30 publications

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“…[11][12][13][14] Compared with the traditional finite element method (FEM) commonly used in topology optimization, the boundary element method (BEM) seems to be more favorable when optimizing the distribution of sound-absorbing materials in the exterior sound field, [15][16][17][18] since only the boundaries need to be discretized and the Sommerfeld boundary condition is automatically satisfied. [19][20][21] Similarly, the BEM is used in many situations. [22][23][24][25][26] The traditional topology optimization finds the optimal solution at a specific frequency, and thus the results may not work for another frequency.…”

Section: Introductionmentioning

confidence: 99%

“…Topology optimization technology is one of the powerful tools to find the optimal distribution of sound‐absorbing materials 11‐14 . Compared with the traditional finite element method (FEM) commonly used in topology optimization, the boundary element method (BEM) seems to be more favorable when optimizing the distribution of sound‐absorbing materials in the exterior sound field, 15‐18 since only the boundaries need to be discretized and the Sommerfeld boundary condition is automatically satisfied 19‐21 . Similarly, the BEM is used in many situations 22‐26 .…”

Section: Introductionmentioning

confidence: 99%

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A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Chen,

Zhao,

Lian

et al. 2023

Numerical Meth Engineering

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In this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Chen,

Zhao,

Lian

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Based on the classical integral equation and fundamental solution, the boundary element method (BEM) has developed rapidly as a powerful numerical tool and has been widely applied to boundary value problems in engineering fields. The BEM distinguishes itself by reducing the spatial dimension in comparison with other numerical calculation methods, [18][19][20][21] which implies that only the boundary needs to be discretized. By aid of the advantage of dimension reduction, many researchers have also extended the BEM to the calculation of the dispersion relation of PCs.…”

Section: Introductionmentioning

confidence: 99%

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

Wei

Xiang

Zhu

et al. 2023

Numerical Meth Engineering

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A novel method of combination of wavelet‐based boundary element method (WBEM) with frequency‐independent fundamental solutions is proposed to determine the band structures of fluid–solid phononic crystals (PCs) with square and triangular lattices. Integral equations established are based on the frequency‐independent fundamental solutions, which can avoid nonlinear eigenvalue problems and reduce computing time. Domain integral terms arising from the use of frequency‐independent fundamental solutions are handled with the radial integration method (RIM) and dual reciprocity method (DRM), respectively. The results show the lower precision in high frequency domain of using RIM to handle domain integral terms than that of using DRM, which can be solved by increasing Gauss point. The B‐spline wavelet on the interval and wavelet coefficients are applied to approximate the physical boundary conditions. It is proved that coupling conditions between matrix and scatterers and Bloch theorem are also applicable to wavelet coefficients. Some small matrix entries generated by wavelet vanishing moment characteristics are truncated by the provided matrix compression technique, and the influence of compressed matrices on the results is studied. Furthermore, the final Eigen equations constructed are modified to avoid numerical instability. Some examples are provided to demonstrate the accuracy and efficiency of the proposed method.

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A density-based topology optimization method using radial basis function and its design variable reduction

Shi

Zhou

2021

Struct Multidisc Optim

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A level-set topological optimization method to analyze two-dimensional thermal problem using BEM

Cited by 16 publications

References 30 publications

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

Band structures analysis of fluid–solid phononic crystals using wavelet‐based boundary element method and frequency‐independent fundamental solutions

A density-based topology optimization method using radial basis function and its design variable reduction

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