Liu, Wing Kam; Jun, Sukky; Zhang, Yi Fei 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 in 1 ReviewCited in 799 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 PDF BibTeX XML Cite \textit{W. K. Liu} et al., Int. J. Numer. Methods Fluids 20, No. 8--9, 1081--1106 (1995; Zbl 0881.76072) 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.