Application of new fast multipole boundary integral equation method to crack problems in 3D

Nishimura, Naoshi; Kobayashi, Shoichi

doi:10.1016/s0955-7997(01)00030-3

Cited by 84 publications

(110 citation statements)

References 20 publications

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“…The boundaries of the model are discretized using boundary elements and the internal domain where local yielding is expected to occur are discretized using internal cells. Then an adaptive quad-tree structure is constructed [18,19,22,24]. The root of the tree, which is at level 0, is a square box containing all the boundaries elements and internal cells.…”

Section: Numerical Implementation Of the Fast Multipole Methodsmentioning

confidence: 99%

“…Usually an expansion of the form in Equation (9) is valid when the locations of the source point x and the field point Y satisfy a certain condition. A typical one is |Y − Y 0 |<|x − Y 0 | [18,19,24].…”

Section: Multipole Expansionmentioning

confidence: 99%

“…The matrix-vector product is obtained by recursive operations on the tree structure without explicitly forming the coefficient matrix. In recent years, the fast multipole BEM and its applications were investigated by many authors, including Peirce and Napier [16] for 2D elastostatics, Popov and Power [17] for 3D elastostatics, Yoshida et al [18,19] for 3D elastostatic crack problems, Liu et al [20] for the modelling of carbon-nanotube composites, Wang and Yao [21,22] for the simulation of composite materials, and Wang and Yao [23] for the analysis of fatigue crack growth. A recent literature review on the fast multipole BEM has been given by Nishimura [24].…”

Section: Introductionmentioning

confidence: 99%

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Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Wang¹,

Yao²

2006

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents a fast multipole boundary element method (BEM) for the analysis of two-dimensional elastoplastic problems. An incremental iterative technique based on the initial strain approach is employed to solve the nonlinear equations, and the fast multipole method (FMM) is introduced to achieve higher runtime and memory storage efficiency. Both of the boundary integrals and domain integrals are calculated by recursive operations on a quad-tree structure without explicitly forming the coefficient matrix. Combining multipole expansions with local expansions, computational complexity and memory requirement of the matrix-vector multiplication are both reduced to O(N ), where N is the number of degrees of freedom (DOFs). The accuracy and efficiency of the proposed scheme are demonstrated by several numerical examples.

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Section: Numerical Implementation Of the Fast Multipole Methodsmentioning

confidence: 99%

Section: Multipole Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Wang¹,

Yao²

2006

Commun. Numer. Meth. Engng.

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“…Therefore, the coupling equation (6) The fast multipole (FM) can accelerate matrix-vector multiplications, which can be used to an iterative solver for the solution of the linear equation (5) and (6). And the memory requirement can be reduced without computing coefficient matrix.…”

Section: Formulation Of Open Floating Potential Electrostatic Promentioning

confidence: 99%

“…Preconditioner based on the block diagonal matrix corresponding to the non-interacting particles for 3D many particle problems is found to be fewer iteration numbers [5]. a preconditioner is well suited for fast multipole BEM to the analysis of 3D crack problems [6]. The preconditioning of fast multipole BEM has been solved successfully by a new technique based on the inverse of the block diagonal matrix corresponding to element or node neighbors with satisfactory rate of convergence in modeling electron guns [7].…”

Section: Introductionmentioning

confidence: 99%

Application of a Fast Boundary Element Algorithm for Open Floating Potential Electrostatic Problem

Deng¹,

Li²,

Hao³

et al. 2013

IJMO

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Boundary Integral Equation Methods for Elastic and Plastic Problems

Bonnet

2004

Encyclopedia of Computational Mechanics

171

315

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This chapter deals with formulations based on boundary integral equations (BIEs) for elastic and plastic problems. After a brief review of the basic integral identities of solid mechanics and issues associated with the singular character of the fundamental solutions, the collocation and symmetric Galerkin BIE formulations and the associated boundary element methods (BEMs) are presented, in their conventional form where the complete matrix equation is set up using numerical integration and stored. This approach being inadequate for large problem sizes, fast solution techniques are then reviewed, with emphasis on the fast multipole method. Next, BEMs in both collocation and symmetric Galerkin form are described for fracture mechanics and small‐strain elastoplasticity. The treatment of the hypersingular integrals arising in the integral representation of tractions on the crack surface or of strains at potentially plastic interior points is discussed, along with other issues. Shape sensitivity analysis techniques are also presented, based on either the direct differentiation of the primary elastic BIE or an adjoint solution. Finally, the symmetric Galerkin BIE is used to define a symmetric formulation for BEM–FEM coupling.

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Application of new fast multipole boundary integral equation method to crack problems in 3D

Cited by 84 publications

References 20 publications

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Fast multipole boundary element analysis of two‐dimensional elastoplastic problems

Application of a Fast Boundary Element Algorithm for Open Floating Potential Electrostatic Problem

Boundary Integral Equation Methods for Elastic and Plastic Problems

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