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Reproducing kernel particle methods.(English)Zbl 0881.76072

Int. J. Numer. Methods Fluids 20, No. 8-9, 1081-1106 (1995).

The authors develop an approach to the title problem by using the mesh- or grid-free interpolation functions, the dilation and translation of window functions, and the technique of integral window transforms.

Reviewer: L.M.Srivastava (Darussalam)

Cited in1 Review

Cited in1096 Documents

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76R50	Diffusion
76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics

Keywords:

grid-free interpolation functions;dilation;translation;integral window transforms

Cite Review PDF

Full Text:DOI

References:

[1]	Lucy, A. J. 82 pp 1013– (1977)
[2]	Gingold, Mon. Not. R. Astron. Soc. 181 pp 275– (1977) ·Zbl 0421.76032 ·doi:10.1093/mnras/181.3.375
[3]	Nayroles, Comput. Mech. 10 pp 307– (1992)
[4]	Belytschko, Int. numer. methods eng. 37 pp 229– (1994)
[5]	Lancaster, Math. Comput. 37 pp 141– (1981)
[6]	and , ’Smooth particle hydrodynamics with strength of materials’, Lecture Notes in Physics, Vol. 395, Advances in the Free-Lagrange Method, Springer, Berlin, 1990, pp. 248-257.
[7]	and , ’Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations’, Preprint, 1993.
[8]	An Introduction to Wavelets, Academic, New York, 1992. ·Zbl 0925.42016
[9]	CBMS/NSF Series in Applied Mathematics, No. 61, Ten Lectures on Wavelets, SIAM, Philadelphia, PA, 1992. ·Zbl 0776.42018 ·doi:10.1137/1.9781611970104
[10]	Liu, Int. j. numer. methods. eng. 38 pp 1655– (1995)
[11]	and , ’Wavelet and multiple scale reproducing kernel methods’, Int. j. numer. methods fluids, (1995). ·Zbl 0885.76078
[12]	Monaghan, SIAM J. Sci. Stat. Comput. 3 pp 422– (1982)
[13]	Monaghan, Comput. Phys. Commun. 48 pp 89– (1988)
[14]	The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, NJ, 1974. ·Zbl 0375.65052
[15]	Liu, Int. j. numer. methods eng. 32 pp 969– (1991)
[16]	Brooks, Comput. Methods Appl. Mech. Eng. 32 pp 199– (1982)
[17]	Hughes, Comput. Methods Appl. Mech. Eng. 45 pp 217– (1984)

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.