An efficient accurate Local Method of Approximate Particular Solutions for solving convection-diffusion problems

C. A. Bustamante, H. Power, W. F. Florez

    Research output: Contribution to journalArticlepeer-review

    8 Scopus citations

    Abstract

    An efficient accurate Local Method of Approximate Particular Solutions (LMAPS) using Multiquadric Radial Basis Functions (RBFs) for solving convection-diffusion problems is proposed. It consists in adding auxiliary points to the local interpolation stencil at which the governing PDE is enforced, known as PDE points, besides imposing the boundary condition at the stencil in contact with the problem boundary. Two convection-diffusion problems are considered as test problems and solved with two previous local direct RBF collocation schemes (with and without PDE points) and two LMAPS (with and without PDE points), as well as the Global MAPS, in order to compare accuracy, convergence order and their behaviour in terms of the shape parameter. If PDE points are added, the result accuracy is improved as well as the convergence rate when using both local direct and MAPS formulations.

    Original languageEnglish
    Pages (from-to)32-37
    Number of pages6
    JournalEngineering Analysis with Boundary Elements
    Volume47
    Issue number1
    DOIs
    StatePublished - Oct 2014

    Keywords

    • Convection-diffusion equation
    • Meshless methods
    • Particular solutions
    • Radial basis functions

    Fingerprint

    Dive into the research topics of 'An efficient accurate Local Method of Approximate Particular Solutions for solving convection-diffusion problems'. Together they form a unique fingerprint.

    Cite this