A new meshless interpolation scheme for MLPG_R method

Article English OPEN
Ma, Q. (2008)
  • Publisher: TECH SCIENCE PRESS
  • Subject: TC

In the MLPG{\_}R (Meshless Local Petrove-Galerkin based on Rankine source solution) method, one needs a meshless interpolation scheme for an unknown function to discretise the governing equation. The MLS (moving least square) method has been used for this purpose so far. The MLS method requires inverse of matrix or solution of a linear algebraic system and so is quite time-consuming. In this paper, a new scheme, called simplified finite difference interpolation (SFDI), is devised. This scheme is generally as accurate as the MLS method but does not need matrix inverse and consume less CPU time to evaluate. Although this scheme is purposely developed for the MLPG{\_}R method, it may also be used for other meshless methods.
  • References (8)

    Atluri ,S.N.; Shen ,S. (2002): The Meshless Local PetroveGalerkin (MLPG) Method: A Simple & Less-costly Alternative to the Finite Element and Boundary Element Methods, CMES: Computer Modeling in Engineering & Sciences, Vol. 3 (1), pp. 11-52.

    Atluri, S.N.; Zhu, T. (1998): A New Meshless Local PetrovGalerkin (MLPG) Approach in Computational Mechanics, Computational Mechanics, Vol. 22, pp. 117-127.

    Atluri, S.N. (2005): Methods of Computer Modeling in Engineering and the Sciences. Vol. 1, Tech Science Press.

    Atluri, S.N.; Liu, H.T.; Han, Z. D. (2006): Meshless Local Koshizuka, S.; Oka, Y. (1996): Moving-Particle SemiPetrov-Galerkin (MLPG) Mixed Finite Difference Method Implicit Method for Fragmentation of Incompressible for Solid Mechanics, CMES: Computer Modeling in Fluid, Nuclear Science and Engineering, 123, pp. 421-434. Engineering & Sciences, Vol. 15, No.1, pp. 1-16. Koshizuka, S., Ikeda, Y., Oka, Y., (1999): Numerical Chen, J. K.; Beraun, J. E. (2000): A generalized smoothed analysis of fragmentation mechanisms in vapour particle hydrodynamics method for nonlinear dynamic explosions, Nuclear Engineering and Design, 189, pp. problems, Computer Methods in Applied Mechanics and 423-433.

    Engineering, Vol. 190, Issues 1-2, pp. 225-239. Liszka, T. J.; Duarte, C. A. M.; Tworzydlo, W. W. (1996): Faure, H. (1990): Using permutations to reduce discrepancy. hp-Meshless cloud method, Computer Methods in Applied J. Comp. Appl. Math., 31:97-103, 1990. Mechanics and Engineering, Vol. 139, 263-288.

    Han, Z. D.; Atluri, S. N. (2004a): Meshless Local Petrov- Ma, Q.W., (2005a): Meshless Local Petrov-Galerkin Method Galerkin (MLPG) Approach for 3-Dimensional Elasto- for Two-dimensional Nonlinear Water Wave Problems. dynamics, Computers, Materials & Continua, Vol. 1 (2), Journal of Computational Physics, Vol. 205, Issue 2, pp. pp. 129-140. 611-625.

    Han, Z. D.; Atluri, S. N. (2004b): Meshless Local Petrov- Ma, Q.W., (2005b): MLPG Method Based on Rankine Galerkin (MLPG) Approaches for Solving 3D Problems in Source Solution for Simulating Nonlinear Water Waves, Elasto-statics, CMES: Computer Modeling in Engineering CMES: Computer Modeling in Engineering & Sciences, & Sciences, Vol. 6 (2), pp. 169-188. Vol. 9, No. 2, pp. 193-210.

    Heo, S., Koshizuka, S. and Oka, Y., (2002): Numerical Yoon, H.Y., Koshizuka, S., Oka, Y., (2001): Direct analysis of boiling on high heat-flux and high sub-cooling calculation of bubble growth, departure, and rise in condition using MPS-MAFL, International Journal of nucleate pool boiling, International Journal of Multiphase Heat and Mass Transfer, 45, pp. 2633-2642. Flow, 27, pp. 277-298.

  • Metrics
    0
    views in OpenAIRE
    0
    views in local repository
    59
    downloads in local repository

    The information is available from the following content providers:

    From Number Of Views Number Of Downloads
    City Research Online - IRUS-UK 0 59
Share - Bookmark