Seamless integration of computer-aided geometric modeling and acoustic simulation: Isogeometric boundary element methods based on Catmull-Clark subdivision surfaces

This paper proposes a novel optimization framework in passive control techniques to reduce noise pollution. The geometries of the structures are represented by Catmull-Clark subdivision surfaces, which are able to build gap-free Computer-Aided Design models and meanwhile tackle the extraordinary points that are commonly encountered in geometric modelling. The acoustic fields are simulated using the isogeometric boundary element method, and a density-based topology optimization is conducted to optimize distribution of sound-absorbing materials adhered to structural surfaces. The approach enables one to perform acoustic optimization from Computer-Aided Design models directly without needing meshing and volume parameterization, thereby avoiding the geometric errors and time-consuming preprocessing steps in conventional simulation and optimization methods. The effectiveness of the present method is demonstrated by three dimensional numerical examples.

Section: Introductionmentioning

confidence: 99%

“…This may be attributed to its simplicity, generality, and well-established ecosystem. Although the Catmull-Clark subdivision surfaces have been successfully incorporated into IGABEM for numerical simulation [15,38], to the best of our knowledge, no study has been reported on topology optimization thus far.…”

Section: Introductionmentioning

confidence: 99%

Noise Pollution Reduction through a Novel Optimization Procedure in Passive Control Methods

Lian¹,

Chen²,

Lin³

et al. 2022

“…Because both the BEM and CAD are based on boundary representation [5][6][7], they are naturally compatible with each other. IGA in the context of the boundary element method (IGABEM) has been successfully applied to a wide range of areas, including potential problems [8], linear elasticity [9,10], fracture mechanics [11][12][13][14], structural optimization [15][16][17][18], acoustics [19][20][21][22][23][24][25], and heat conduction [26,27], etc.…”

Section: Introductionmentioning

confidence: 99%

Machine Learning Enhanced Boundary Element Method: Prediction of Gaussian Quadrature Points

Cheng¹,

Yin²,

Chen³

2022

This paper applies a machine learning technique to find a general and efficient numerical integration scheme for boundary element methods. A model based on the neural network multi-classification algorithm is constructed to find the minimum number of Gaussian quadrature points satisfying the given accuracy. The constructed model is trained by using a large amount of data calculated in the traditional boundary element method and the optimal network architecture is selected. The two-dimensional potential problem of a circular structure is tested and analyzed based on the determined model, and the accuracy of the model is about 90%. Finally, by incorporating the predicted Gaussian quadrature points into the boundary element analysis, we find that the numerical solution and the analytical solution are in good agreement, which verifies the robustness of the proposed method.

“…Wang et al [11] solved the three-dimensional elasto-plastic problem by boundary element method. On the contrary, boundary element method (BEM) [12][13][14][15][16][17][18][19] only needs boundary parameterization and thus is compatible with CAD models naturally. The isogeometric analysis with boundary element method (IGABEM) was first applied to potential problems [20] and elasticity analysis [21,22].…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Boundary ElementAnalysis for 2DTransientHeat Conduction Problem with Radial Integration Method

Chen¹,

Li²,

Peng³

et al. 2021

This paper presents an isogeometric boundary element method (IGABEM) for transient heat conduction analysis. The Non-Uniform Rational B-spline (NURBS) basis functions, which are used to construct the geometry of the structures, are employed to discretize the physical unknowns in the boundary integral formulations of the governing equations. Bézier extraction technique is employed to accelerate the evaluation of NURBS basis functions. We adopt a radial integration method to address the additional domain integrals. The numerical examples demonstrate the advantage of IGABEM in dimension reduction and the seamless connection between CAD and numerical analysis.