A general mesh finite difference method using combined nodal and elemental interpolation

Mullord, P.

doi:10.1016/s0307-904x(79)80026-8

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…It is difficult for the analysis by the classical FDM to automatically discretize boundary conditions, especially in the case of arbitrarily shaped domains. However, recently the development of the FDM generalized for arbitrarily unstructured grids (GFDM) [11][12][13][14] clearly indicates its potential power, which is comparable with the finite element method (FEM). It is shown that the GFDM may not only become equally universal, versatile, and suitable to full automation as the FEM, but also it is even more convenient in some areas of applications [15].…”

Section: Introductionmentioning

confidence: 99%

A gradient smoothing method (GSM) with directional correction for solid mechanics problems

et al. 2007

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A novel gradient smoothing method (GSM) is proposed in this paper, in which a gradient smoothing together with a directional derivative technique is adopted to develop the first-and second-order derivative approximations for a node of interest by systematically computing weights for a set of field nodes surrounding. A simple collocation procedure is then applied to the governing strong-from of system equations at each node scattered in the problem domain using the approximated derivatives. In contrast with the conventional finite difference and generalized finite difference methods with topological restrictions, the GSM can be easily applied to arbitrarily irregular meshes for complex geometry. Several numerical examples are presented to demonstrate the computational accuracy and stability of the GSM for solid mechanics problems with regular and irregular nodes. The GSM is examined in detail by comparison with other established numerical approaches such as the finite element method, producing convincing results.

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Section: Introductionmentioning

confidence: 99%

A gradient smoothing method (GSM) with directional correction for solid mechanics problems

et al. 2007

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An interpolation method for an irregular net of nodes

Liszka¹

1984

Numerical Meth Engineering

188

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SUMMARYA local interpolation method for an irregular mesh of nodal points is proposed. The method is based on a Taylor expansion of the unknown function combined with the minimization of errors. Some numerical tests as well as a computer program are presented. Applicability and stability of the method are shown. By the appropirate definition of weighting coefficients, this method may be viewed as an interpolation or approximation in the sense of minimum deviation from given values. Applications in finite element and finite difference methods are shown.

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