Paper Information

Journal:   SCIENTIA IRANICA   2014 , Volume 21 , Number 3 (TRANSACTIONS A: CIVIL ENGINEERING); Page(s) 492 To 504.
 
Paper: 

MIXED DISCRETE LEAST SQUARE MESHLESS METHOD FOR SOLUTION OF QUADRATIC PARTIAL DIERENTIAL EQUATIONS

 
 
Author(s):  FARAJI S.*, AFSHAR M.H., AMANI J.
 
* SCHOOL OF CIVIL ENGINEERING, IRAN UNIVERSITY OF SCIENCE AND TECHNOLOGY, NARMAK, TEHRAN, IRAN
 
Abstract: 

In this paper, the Mixed Discrete Least Squared Meshless (MDLSM) method is used for solving quadratic Partial Dierential Equations (PDEs). In the MDLSM method, the domain is discretized only with nodes, and a minimization of a least squares functional is carried out. The least square functional is de ned as the sum of the residuals of the governing dierential equation and its boundary condition at the nodal points. In MDLSM, the main unknown parameter and its rst derivatives are approximated independently with the same Moving Least Squares (MLS) shape functions. The solution of the quadratic PDE does not, therefore, require calculation of the complex second order derivatives of MLS shape functions. Furthermore, both Neumann and Dirichlet boundary conditions can be treated and imposed as a Dirichlet type boundary condition, which is applied using a penalty method. The accuracy and eciency of the MDLSM method are tested against three numerical benchmark examples from one-dimensional and two-dimensional PDEs. The results are produced and compared with the irreducible DLSM method and exact analytical solutions, indicating the ability and eciency of the MDLSM method in ecient and eective solution of quadratic PDEs.

 
Keyword(s): DISCRETE LEAST SQUARES MESHLESS, QUADRATIC PARTIAL DIERENTIAL EQUATIONS, MOVING LEAST SQUARES, MIXED MESHLESS, IRREDUCIBLE MESHLESS
 
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