Fast-multipole accelerated singular boundary method for large-scale three-dimensional potential problems

Gu, Yan; Gao, Hongwei; Chen, Wen; Liu, Congjian; Zhang, Chuanzeng; He, Xiaoqiao

doi:10.1016/j.ijheatmasstransfer.2015.06.060

Cited by 22 publications

(4 citation statements)

References 43 publications

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“…Step 3: When x D y, set the singular term as the averaged value of the fundamental solution over an auxiliary boundary, which is defined by the semi-length distance of the source points ( Figure 3 and Equations (19) and (20)).…”

Section: Treatment Of Singular Termsmentioning

confidence: 99%

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A meshless singular boundary method for three‐dimensional elasticity problems

Chen

Gao

et al. 2016

Numerical Meth Engineering

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SUMMARYThis study documents the first attempt to extend the singular boundary method, a novel meshless boundary collocation method, for the solution of 3D elasticity problems. The singular boundary method involves a coupling between the regularized BEM and the method of fundamental solutions. The main idea here is to fully inherit the dimensionality and stability advantages of the former and the meshless and integrationfree attributes of the later. This makes it particularly attractive for problems in complex geometries and three dimensions. Four benchmark 3D problems in linear elasticity are well studied to demonstrate the feasibility and accuracy of the proposed method. The advantages, disadvantages, and potential applications of the proposed method, as compared with the FEM, BEM, and method of fundamental solutions, are also examined and discussed.

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Section: Treatment Of Singular Termsmentioning

confidence: 99%

“…Recently, Chen and his co‐workers have proposed a meshless method that they call the singular boundary method (SBM). The method belongs to the family of meshless boundary collocation methods and can be viewed as one kind of modified method of fundamental solutions (MFS) .…”

Section: Introductionmentioning

confidence: 99%

A meshless singular boundary method for three‐dimensional elasticity problems

Chen

Gao

et al. 2016

Numerical Meth Engineering

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“…The classical MFS approach, however, produces dense and non-symmetric matrix of algebraic equations that requires memory and other operators to compute the unknown coefficients [14][15][16][17][18]. This makes the method limited to solving small-scale problems with thousands of degrees of freedom for a long time [7,[19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

Gu¹,

Fan²,

Fu³

2021

AAMM

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A localized version of the method of fundamental solution (LMFS) is devised in this paper for the numerical solutions of three-dimensional (3D) elasticity problems. The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation. Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations. Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies. The advantages, disadvantages and potential applications of the proposed method, as compared with the classical MFS and boundary element method (BEM), are discussed.

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“…Another effective method, finite element methods, is also widely used for the numerical solution, see [24,25]. Another popular method for the direct and inverse heat conduction problems is the singular boundary method, we can see [26][27][28][29][30] for further reading.…”

Section: Introductionmentioning

confidence: 99%

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

et al. 2019

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In this paper, we give an effective numerical method for the heat conduction problem connected with the Laplace equation. Through the use of a single-layer potential approach to the solution, we get the boundary integral equation about the density function. In order to deal with the weakly singular kernel of the integral equation, we give the projection method to deal with this part, i.e., using the Lagrange trigonometric polynomials basis to give an approximation of the density function. Although the problems under investigation are well-posed, herein the Tikhonov regularization method is not used to regularize the aforementioned direct problem with noisy data, but to filter out the noise in the corresponding perturbed data. Finally, the effectiveness of the proposed method is demonstrated using a few examples, including a boundary condition with a jump discontinuity and a boundary condition with a corner. Whilst a comparative study with the method of fundamental solutions (MFS) is also given.

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Fast-multipole accelerated singular boundary method for large-scale three-dimensional potential problems

Cited by 22 publications

References 43 publications

A meshless singular boundary method for three‐dimensional elasticity problems

A meshless singular boundary method for three‐dimensional elasticity problems

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

A Numerical Method for Filtering the Noise in the Heat Conduction Problem

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