A fast and accurate algorithm for a Galerkin boundary integral method

Wang, J.; Crouch, Steven L.; Mogilevskaya, Sofia G.

doi:10.1007/s00466-005-0702-5

Cited by 17 publications

(12 citation statements)

References 20 publications

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“…., N is required to achieve a necessary degree of accuracy). Future work might include the use of a fast multipole method, such as the one described by Wang et al (2005); it would allow one to consider problems involving a larger number of holes. Other future developments of the method might include incorporation of elastic inhomogeneities.…”

Section: Resultsmentioning

confidence: 99%

Linear viscoelastic analysis of a semi-infinite porous medium

Pyatigorets

Mogilevskaya

Marasteanu

2008

International Journal of Solids and Structures

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This paper considers the problem of a semi-infinite, isotropic, linear viscoelastic half-plane containing multiple, nonoverlapping circular holes. The sizes and the locations of the holes are arbitrary. Constant or time dependent far-field stress acts parallel to the boundary of the half-plane and the boundaries of the holes are subjected to uniform pressure. Three types of loading conditions are assumed at the boundary of the half-plane: a point force, a force uniformly distributed over a segment, a force uniformly distributed over the whole boundary of the half-plane. The solution of the problem is based on the use of the correspondence principle. The direct boundary integral method is applied to obtain the governing equation in the Laplace domain. The unknown transformed displacements on the boundaries of the holes are approximated by a truncated complex Fourier series. A system of linear equations is obtained by using a Taylor series expansion. The viscoelastic stresses and displacements at any point of the half-plane are found by using the viscoelastic analogs of KolosovMuskhelishvili's potentials. The solution in the time domain is obtained by the application of the inverse Laplace transform. All the operations of space integration, the Laplace transform and its inversion are performed analytically. The method described in the paper allows one to adopt a variety of viscoelastic models. For the sake of illustration only one model in which the material responds as the standard solid in shear and elastically in bulk is considered. The accuracy and efficiency of the method are demonstrated by the comparison of selected results with the solutions obtained by using finite element software ANSYS.

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Section: Resultsmentioning

confidence: 99%

Linear viscoelastic analysis of a semi-infinite porous medium

Pyatigorets

Mogilevskaya

Marasteanu

2008

International Journal of Solids and Structures

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“…It is noted that only a fewer inclusions are considered in the demonstrate examples. For large-scale problems (e.g., more than 20 inclusions), fast algorithm [13] is required on the limitation of PC hardware. This is our future study.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…Mogilevskaya and Crouch [12] have also employed Fourier series expansion technique and used the Galerkin method instead of collocation technique to solve the problem of circular inclusions in 2-D elasticity. Also Wang et al [13] proposed a fast algorithm for large-scale problems. The advantage of their method is that one can tackle a lot of inclusions even inclusions touching one another.…”

Section: Introductionmentioning

confidence: 99%

Null-field approach for piezoelectricity problems with arbitrary circular inclusions

Chen

2006

Engineering Analysis with Boundary Elements

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“…Another effort to improve the computational efficiency of the GBEM proposed by Wang et al [254] demonstrated in solving two-dimensional elastostatics problems involving numerous inhomogeneities. Block computation techniques were employed by computing the combined influences of groups of elements using asymptotic expansions, multiple shifts and Taylor series expansions.…”

Section: Galerkin Boundary Element Methodsmentioning

confidence: 99%

Development and implementation of some BEM variants—A critical review

Kadarman

Djojodihardjo

2010

Engineering Analysis with Boundary Elements

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a b s t r a c tDue to rapid development of boundary element method (BEM), this article explores the evolution of BEM over the past half century. We here summarize the overall development and implementation of several well-known BEM variants that includes collocation BEM, galerkin BEM, dual reciprocity BEM, complex variable BEM and analog equation method. Their theoretical and mathematical backgrounds are carefully described and a generalized Laplace's equation (and Poisson's equation) is utilized in demonstrating the different approaches involved. An up-to-date review on characteristics and implementation for each of the five variants is presented and also highlighted their significant contributions in boundary element research. In addition, this article tries to cover whole aspect of interests including efficiency, applicability and accuracy in order to give better understanding of BEM evolution. Comparisons and techniques of improvement for these variants are also discussed.

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A fast and accurate algorithm for a Galerkin boundary integral method

Cited by 17 publications

References 20 publications

Linear viscoelastic analysis of a semi-infinite porous medium

Linear viscoelastic analysis of a semi-infinite porous medium

Null-field approach for piezoelectricity problems with arbitrary circular inclusions

Development and implementation of some BEM variants—A critical review

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