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

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Faraji S.; AFSHAR M.H.; AMANI J.

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Paper Information

Journal: Scientia Iranica Year:2014 | Volume:21 | Issue:3 (TRANSACTIONS A: CIVIL ENGINEERING) Page(s): 492-504

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Information Journal Paper

Title

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

Author(s)

Faraji S. | AFSHAR M.H. | AMANI J. | Issue Writer Certificate

Keywords

DISCRETE LEAST SQUARES MESHLESS

QUADRATIC PARTIAL DIERENTIAL EQUATIONS

MOVING LEAST SQUARES

MIXED MESHLESS

IRREDUCIBLE MESHLESS

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.

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APA: Copy

Faraji, S., AFSHAR, M.H., & AMANI, J.. (2014). MIXED DISCRETE LEAST SQUARE MESHLESS METHOD FOR SOLUTION OF QUADRATIC PARTIAL DIERENTIAL EQUATIONS. SCIENTIA IRANICA, 21(3 (TRANSACTIONS A: CIVIL ENGINEERING)), 492-504. SID. https://sid.ir/paper/290280/en

Vancouver: Copy

Faraji S., AFSHAR M.H., AMANI J.. MIXED DISCRETE LEAST SQUARE MESHLESS METHOD FOR SOLUTION OF QUADRATIC PARTIAL DIERENTIAL EQUATIONS. SCIENTIA IRANICA[Internet]. 2014;21(3 (TRANSACTIONS A: CIVIL ENGINEERING)):492-504. Available from: https://sid.ir/paper/290280/en

IEEE: Copy

S. Faraji, M.H. AFSHAR, and J. AMANI, “MIXED DISCRETE LEAST SQUARE MESHLESS METHOD FOR SOLUTION OF QUADRATIC PARTIAL DIERENTIAL EQUATIONS,” SCIENTIA IRANICA, vol. 21, no. 3 (TRANSACTIONS A: CIVIL ENGINEERING), pp. 492–504, 2014, [Online]. Available: https://sid.ir/paper/290280/en

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