×

zbMATH — the first resource for mathematics

A finite point method in computational mechanics. Applications to convective transport and fluid flow. (English) Zbl 0884.76068
Summary: The paper presents a fully meshless procedure for solving partial differential equations. The approach termed generically the ‘finite point method’ is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals. Some examples showing the accuracy of the method for solution of adjoint and non-self adjoint equations typical of convective-diffusive transport, and also an application to the analysis of a compressible fluid mechanics problem, are presented.

MSC:
76M25 Other numerical methods (fluid mechanics) (MSC2010)
76R99 Diffusion and convection
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] and , The Finite Element Method, McGraw-Hill, New York, Vol. I., 1989, Vol. 2, 1991.
[2] Idelsohn, Int. J. numer. methods eng. 37 pp 3323– (1994) · Zbl 0813.76041 · doi:10.1002/nme.1620371908
[3] Oñate, Int. J. numer. methods eng. 37 pp 181– (1994) · Zbl 0795.73079 · doi:10.1002/nme.1620370202
[4] and , ’Finite elements versus finite volumes. Is there a choice?’, in Non Linear Computational Mechanics. State of the Art, and (eds.), Springer, Berlin, 1991.
[5] MacNeal, Q. Appl. Math. 11 pp 295– (1953) · Zbl 0053.26304 · doi:10.1090/qam/99978
[6] and , Finite Difference Methods for Partial Differential Equations, Wiley, New York, 1960.
[7] Jensen, Comput. Struct. 2 pp 17– (1972) · doi:10.1016/0045-7949(72)90020-X
[8] Perrone, Comput. Struct. 5 pp 45– (1975) · doi:10.1016/0045-7949(75)90018-8
[9] Frey, Int. J. numer. methods eng. 11 pp 1653– (1977) · Zbl 0368.65051 · doi:10.1002/nme.1620111103
[10] Pavlin, Int. J. numer. methods eng. 14 pp 647– (1979) · Zbl 0396.73056 · doi:10.1002/nme.1620140503
[11] Liszka, Comput. Struct. 11 pp 83– (1980) · Zbl 0427.73077 · doi:10.1016/0045-7949(80)90149-2
[12] Liszka, Int. J. numer. methods eng. 20 pp 1594– (1984) · Zbl 0544.65006 · doi:10.1002/nme.1620200905
[13] Nay, Variational Methods Eng. 1 (1972)
[14] Gingold, Man. Not. Roy. Astron. Soc. 181 pp 375– (1977) · Zbl 0421.76032 · doi:10.1093/mnras/181.3.375
[15] Moraghan, SIAM J. Sci., Statist. Comput. 3 pp 422– (1982) · Zbl 0498.76010 · doi:10.1137/0903027
[16] Moraghan, Comput. Phys. Commun. 48 pp 89– (1988) · Zbl 0673.76089 · doi:10.1016/0010-4655(88)90026-4
[17] and , (eds.), Advances in the Free Lagrange Method, Lecture Notes in Physics, Springer, Berlin, 1990.
[18] Liu, Int. J. numer. methods fluids 20 pp 1081– (1995) · Zbl 0881.76072 · doi:10.1002/fld.1650200824
[19] Nayroles, Comput. Mech. 10 pp 307– (1992) · Zbl 0764.65068 · doi:10.1007/BF00364252
[20] Belytschko, Int. J. numer. methods eng. 37 pp 229– (1994) · Zbl 0796.73077 · doi:10.1002/nme.1620370205
[21] Lu, Comput. Methods Appl. Mech. Eng. 113 pp 397– · Zbl 0847.73064 · doi:10.1016/0045-7825(94)90056-6
[22] and , ’Hp clouds-A meshless method to solve boundary-value problems’, TICAM Repport 95-05, May 1995.
[23] and , ’The partition of unity finite element method’, Technical Note EN-1185, Institute for Physical Science and Technology, Univ. Maryland, April 1995.
[24] Liu, Int. J. numer. methods eng. 38 pp 1655– (1195) · Zbl 0840.73078 · doi:10.1002/nme.1620381005
[25] and , ’Wavelet and multiple scale producing Kernel methods’, Int. J. numer. methods fluids, (1995) in print.
[26] , , , , , and , ’Overview and applications of the Reproducing Kernel particle methods’, Arch. Comput. Methods Eng., in print, 1996.
[27] ’A review some meshless methods to solve partial differetial equations’, TICAM Report 95-06, The Univ. of Texas, Austin, May 1995.
[28] and , ’Finite point methods in computational mechanics’, Research Report No. 67, CIMNE, Barcelona, July 1995.
[29] ’A gridless Euler/Navier-Stokes solution algorithm for complex aircraft applications’, AIAA 93-0333, Reno NV, January 11-14, 1993.
[30] Brooks, Comput. Methods Appl. Mech. Eng. 32 (1982) · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[31] Codina, Comput. Methods Appl. Mech. Eng. 94 (1992) · Zbl 0748.76082 · doi:10.1016/0045-7825(92)90149-E
[32] Numerical Computations of Internal and External Flows, Vol. 2, Wiley, New York, 1990.
[33] and , ’A meshless method for analysis of high speed flows’, AGARD Meeting, Seville, October 1995.
[34] , and , ’A finite point method for analysis of fluid flow problems’, Proc. 9th Int. Conf. on Finite Element Methods in Fluids, Venize, Italy, 15-21, October 1995.
[35] Zienkiewicz, Int. J. numer. methods fluids 20 pp 869– (1995) · Zbl 0837.76043 · doi:10.1002/fld.1650200812
[36] Peraire, Int. J. numer. methods eng. 26 pp 2135– (1988) · Zbl 0665.76073 · doi:10.1002/nme.1620261002
[37] , and , ’Moving least square approximations for solution of differential equations’, Research Report no 74, CIMNE, Barcelona, December 1995.
[38] Oñate, Comp. Meth. Appl. Mech. Eng.
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.