Alternating direction method for the Poisson equation with variable weight coefficients in an integral condition

2011 ◽  
Vol 47 (8) ◽  
pp. 1176-1187 ◽  
Author(s):  
M. Sapagovas ◽  
A. Štikonas ◽  
O. Štikonienė
Keyword(s):  
Poisson Equation ◽  
Integral Condition ◽  
Alternating Direction Method ◽  
The Poisson Equation ◽  
Alternating Direction ◽  
Variable Weight ◽  
Weight Coefficients

scholarly journals A LOCAL DIFFERENTIAL QUADRATURE METHOD WITH VARIABLE SHAPE MULTIQUADRICS: TESTS ON POISSON EQUATION AND FLUID DYNAMICS USING CONSISTENT CLOUD REFINEMENTS

2017 ◽  
Vol 16 (2) ◽  
pp. 62
Author(s):  
J. R. da Silva ◽  
L. G. C. Santos ◽  
N. Manzanares Filho
Keyword(s):  
Poisson Equation ◽  
Point Cloud ◽  
Shape Parameter ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Basis Set ◽  
Quadrature Method ◽  
Square Cavity ◽  
The Poisson Equation ◽  
Weight Coefficients

A meshless Local Differential Quadrature Method for solving partial differential equations is presented in this paper. It is based in a point cloud discretization and local supports. A basis set of Multiquadric functions is employed for determining the weight coefficients in derivative approximations. Tests with the Poisson equation are presented for verifying the converge behavior of the method in Clouds with Unstructured Generation (CUG’s). A consistent refinement procedure for varying the multiquadric shape parameter between local supports is proposed. The method is finally applied for solving the classical benchmark problem of natural convection in a square cavity. Satisfactory results were obtained in comparison with the reference literature.

scholarly journals Alternating direction method for two-dimensional parabolic equation with nonlocal integral condition

2012 ◽  
Vol 17 (1) ◽  
pp. 91-98 ◽  
Author(s):  
Mifodijus Sapagovas ◽  
Kristina Jakubėlienė
Keyword(s):  
Parabolic Equation ◽  
Nonlocal Condition ◽  
Integral Condition ◽  
Rectangular Domain ◽  
Alternating Direction Method ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Alternating Direction ◽  
Nonlocal Integral Condition ◽  
Dimensional Domain

Two-dimensional parabolic equation with nonlocal condition is solved by alternating direction method in the rectangular domain. Values of the solution on the boundary points are bind with the integral of the solution in whole two-dimensional domain. Because of this nonlocal condition, the classical alternating direction method is complemented by the solution of low dimension system of algebraic equations. The peculiarities of the method are considered.

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