QUT ePrints

An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Gu, YuanTong (2010) An advanced implicit meshless approach for fractional partial differential equation in computational mechanics. In Howard, Ian, Teh, Kian, & Davies, Ian (Eds.) Proceedings from the 6th Australasian Congress on Applied Mechanics, Engineers Australia, Perth Convention Exhibition Centre, Perth, WA, pp. 1-8.

[img] pending for publisher permission (PDF 991kB)
Accepted Version.
Administrators only | Request a copy from author

    View at publisher

    Abstract

    Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

    Impact and interest:

    Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

    These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

    Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

    ID Code: 40084
    Item Type: Conference Paper
    Keywords: Fractional Partial Differential Equation, FDM, FEM, Meshless, RBF
    ISBN: 9780858259416
    ISSN: 1448-4846
    Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
    Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
    Past > Schools > School of Engineering Systems
    Copyright Owner: Copyright 2010 Engineers Australia
    Deposited On: 07 Mar 2011 08:24
    Last Modified: 01 Mar 2012 00:30

    Export: EndNote | Dublin Core | BibTeX

    Repository Staff Only: item control page