A self-adaptive h-refinement technique for the boundary element method

Rencis, Joseph J.; Jong, K.-Y.

doi:10.1016/0045-7825(89)90070-4

Cited by 40 publications

(1 citation statement)

References 25 publications

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“…Since the proposed meshless method does not explicitly involve meshes, this method provides a convenient implementation of adaptive process by simply adding or deleting nodes. An adaptive algorithm is developed in this research based on the projection technique for error analysis in the FEM [30], the BEM [31] and the element-free Galerkin method [32].…”

Section: Example 2: Singular Problemmentioning

confidence: 99%

A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

Zhu

Zhang

2011

Applied Mathematical Modelling

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a b s t r a c t This paper presents a meshless method, which replaces the inhomogeneous biharmonic equation by two Poisson equations in terms of an intermediate function. The solution of the Poisson equation with the intermediate function as the right-hand term may be written as a sum of a particular solution and a homogeneous solution of a Laplace equation. The intermediate function is approximated by a series of radial basis functions.Then the particular solution is obtained via employing Kansa's method, while the homogeneous solution is approximated by using the boundary radial point interpolation method by means of boundary integral equations. Besides, the proposed meshless method, in conjunction with the analog equation method, is further developed for solving generalized biharmonic-type problems. Some numerical tests illustrate the efficiency of the method proposed.

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Section: Example 2: Singular Problemmentioning

confidence: 99%

A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

Zhu

Zhang

2011

Applied Mathematical Modelling

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An adaptive h‐r boundary element algorithm for the laplace equation

Sun

Zamani

1992

Numerical Meth Engineering

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SUMMARYIn this paper, the combination of the h-method (mesh refinement) and the r-method (mesh redistribution) is employed to solve the Laplace equation using the boundary element procedure. The key in this approach is to derive on upper bound for the residual associated with the boundary element solution and minimize this bound with respect to an unknown grading function. The latter part is achieved by employing techniques of the calculus of variations.

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Error Estimation and Adaptivity in the Boundary Element Method

Liapis

1995

Computational Mechanics ’95

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A self-adaptive h-refinement technique for the boundary element method

Cited by 40 publications

References 25 publications

A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

An adaptive h‐r boundary element algorithm for the laplace equation

Error Estimation and Adaptivity in the Boundary Element Method

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