Full Multigrid Method for Solving the General Three Dimensional Elliptic Partial Differential Equation with Variable Coefficients and with General Boundary Conditions

Osama El-Giar

doi:https://doi.org/10.14445/22315373/IJMTT-V18P502

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 18 | Number 1 | Year 2015 | Article Id. IJMTT-V18P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V18P502

Full Multigrid Method for Solving the General Three Dimensional Elliptic Partial Differential Equation with Variable Coefficients and with General Boundary Conditions

Osama El-Giar

Citation :

Osama El-Giar, "Full Multigrid Method for Solving the General Three Dimensional Elliptic Partial Differential Equation with Variable Coefficients and with General Boundary Conditions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 18, no. 1, pp. 7-13, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V18P502

Abstract

In this paper we apply a full multigrid method with a W(r1,r2)cycle to obtain the numerical solution of the three dimensional general elliptic partial differential equation with variable coefficients and with general boundary conditions (Robbin’s and Neumann’s boundary conditions) in a unit cube. Red-black gauss-Seidel iteration is used for relaxation process, linear interpolation is used to transfer the correction values from coarse grids to fine grids and half weighting restriction process is used to restrict the residuals from fine grids to coarse grids. Numerical examples have been given to illustrate the efficiency of this method.

Keywords

Multigrid method, Numerical Analysis, Three Dimensional General Elliptic Partial Differential Equation, Robin’s and Neumann’s Boundary conditions.

References

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