NDLI: The meshless analog equation method: I. Solution of elliptic partial differential equations

Content Provider	Springer Nature Link
Author	Katsikadelis, John T.
Copyright Year	2008
Abstract	A new purely meshless method for solving elliptic partial differential equations (PDEs) is presented. The method is based on the principle of the analog equation of Katsikadelis, hence its name meshless analog equation method (MAEM), which converts the original equation into a simple solvable substitute one of the same order under a fictitious source. The fictitious source is represented by multiquadric radial basis functions (MQ-RBFs). The integration of the analog equation yields new RBFs, which are used to approximate the sought solution. Then inserting the approximate solution into the PDE and boundary conditions (BCs) and collocating at the mesh-free nodal points results in a system of linear equations, which permit the evaluation of the expansion coefficients of the RBFs series. The method exhibits key advantages over other RBF collocation methods as it is highly accurate and the coefficient matrix of the resulting linear equations is always invertible. The accuracy is achieved using optimal values for the shape parameters and the centers of the multiquadrics as well as of the integration constants of the analog equation, which are obtained by minimizing the functional that produces the PDE. Without restricting its generality, the method is illustrated by applying it to the general second order 2D and 3D elliptic PDEs. The studied examples demonstrate the efficiency and high accuracy of the developed method.
Starting Page	557
Ending Page	578
Page Count	22
File Format	PDF
ISSN	09391533
Journal	Archive of Applied Mechanics
Volume Number	79
Issue Number	6
e-ISSN	14320681
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-01-13
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Meshless method Elliptic partial differential equations Radial basis functions Analog equation method Mechanics Theoretical and Applied Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering

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