TITLE:
High Order Compact Difference Scheme and Multigrid Method for 2D Elliptic Problems with Variable Coefficients and Interior/Boundary Layers on Nonuniform Grids
AUTHORS:
Bin Lan, Yongbin Ge, Yan Wang, Yong Zhan
KEYWORDS:
Elliptic Equation, Coordinate Transformation, High Order Compact Difference Scheme, Multigrid Method, Interior/Boundary Layer
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.5,
May
19,
2015
ABSTRACT: In this
paper, a high order compact difference scheme and a multigrid method are
proposed for solving two-dimensional (2D) elliptic problems with variable
coefficients and interior/boundary layers on nonuniform grids. Firstly, the
original equation is transformed from the physical domain (with a nonuniform
mesh) to the computational domain (with a uniform mesh) by using a coordinate
transformation. Then, a fourth order compact difference scheme is proposed to
solve the transformed elliptic equation on uniform girds. After that, a
multigrid method is employed to solve the linear algebraic system arising from
the difference equation. At last, the numerical experiments on some elliptic
problems with interior/boundary layers are conducted to show high accuracy and high
efficiency of the present method.