Thermal analysis of 3D composites by a new fast multipole hybrid boundary node method

Miao, Yu; Wang, Qiao; Zhu, Hongping; Li, Yinping

doi:10.1007/s00466-013-0893-0

Cited by 17 publications

(2 citation statements)

References 34 publications

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“…Meshless (mesh-free) methods have been developed in the past decades to reduce the required effort for mesh generation. Many meshless methods have been proposed thus far, including the smoothed particle hydrodynamics (SPH) method [6,7], the reproducing kernel particle methods (RKPM) [8], the hpclouds method [9], the element-free Galerkin method (EFG) [10], the meshless local Petrov-Galerkin (MLPG) approach [11], the boundary node method (BNM) [12][13][14], the boundary element-free method (BEFM) [15], the hybrid boundary node method (hybrid BNM) [16][17][18][19][20], the Galerkin boundary node method (GBNM) [21], the boundary face method (BFM) [22,23], and the boundary point interpolation method [24].…”

Section: Introductionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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The presented study proposed an improved interpolating boundary node method (IIBNM) for 2D potential problems. The improved interpolating moving least-square (IIMLS) method was applied to construct the shape functions, of which the delta function properties and boundary conditions were directly implemented. In addition, any weight function used in the moving least-square (MLS) method was also applicable in the IIMLS method. Boundary cells were required in the computation of the boundary integrals, and additional discretization error was not avoided if traditional cells were used to approximate the geometry. The present study applied the parametric cells created in the parameter space to preserve the exact geometry, and the geometry was maintained due to the number of cells. Only the number of nodes on the boundary was required as additional information for boundary node construction. Most importantly, the IIMLS method can be applied in the parameter space to construct shape functions without the requirement of additional computations for the curve length.

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Section: Introductionmentioning

confidence: 99%

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Yang

Chen

2017

Mathematical Problems in Engineering

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“…The first type is formed by combining the moving least-square approximation with boundary integral equation methods. Excellent researches include the boundary node method [1,2], local boundary integral equation method (LBIE) [3][4][5][6], improved boundary node method [7][8][9][10][11], and boundary element-free method (BEFM) [12][13][14][15]. These methods have been successfully applied to many engineering problems; take the potential problem and elasticity problem as examples [16,17].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

Wang

Zheng

2014

Mathematical Problems in Engineering

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Numerical solutions of the boundary knot method (BKM) always perform oscillatory convergence when using a large number of boundary points in solving the Helmholtz-type problems. The main reason for this phenomenon may contribute to the severely ill-conditioned full coefficient matrix. In order to obtain admissible stable convergence results, regularization techniques and the effective condition number are employed in the process of simulating 3D Helmholtz-type problems. Numerical results are tested for the 3D Helmholtz-type equation with noisy and non-noisy boundary conditions. It is shown that the BKM in combination with the regularization techniques is able to produce stable numerical solutions.

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A fast multipole accelerated indirect boundary element method for broadband scattering of elastic waves in a fluid‐saturated poroelastic domain

Liu

Sun

Cheng

et al. 2018

Num Anal Meth Geomechanics

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Summary A fast multipole accelerated indirect boundary element method is developed to efficiently solve the scattering of broadband waves by inhomogeneity in a fluid‐saturated 3D poroelastic space. Based on the single layer potential theory, poroelastic free‐space Green's functions of point force and fluid source are distributed on the scatterer surface at fictitious densities to construct the scattered waves. By using the plane wave expansion of 3D potential functions of compressional and shear waves, the multipole expansion and the local expansion coefficients are derived. Numerical results demonstrated that this proposed method can greatly improve the efficiency of traditional indirect boundary element method and reduce the memory requirement for 3D broadband wave scattering problems in an unbounded poroelastic medium. Problems of wave scattering by a spherical cavity, a group of cavities, and a canyon in a semiinfinite poroelastic space are investigated. Several notable scattering characteristics are revealed.

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Thermal analysis of 3D composites by a new fast multipole hybrid boundary node method

Cited by 17 publications

References 34 publications

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

A General 2D Meshless Interpolating Boundary Node Method Based on the Parameter Space

Analysis of the Boundary Knot Method for 3D Helmholtz-Type Equation

A fast multipole accelerated indirect boundary element method for broadband scattering of elastic waves in a fluid‐saturated poroelastic domain

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