An unstructured multigrid method for elliptic problems

1987 ◽  
Vol 24 (1) ◽  
pp. 101-115 ◽  
Author(s):  
R. Löhner ◽  
K. Morgan
Keyword(s):  
Multigrid Method ◽  
Elliptic Problems

scholarly journals High-Order Compact Difference Scheme and Multigrid Method for Solving the 2D Elliptic Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Yongbin Ge
Keyword(s):  
Difference Scheme ◽  
Multigrid Method ◽  
Elliptic Problems ◽  
High Order ◽  
Compact Difference Scheme ◽  
Central Difference ◽  
Present Scheme ◽  
Compact Difference ◽  
Compact Approximations ◽  
Error Terms

A high-order compact difference scheme for solving the two-dimensional (2D) elliptic problems is proposed by including compact approximations to the leading truncation error terms of the central difference scheme. A multigrid method is employed to overcome the difficulties caused by conventional iterative methods when they are used to solve the linear algebraic system arising from the high-order compact scheme. Numerical experiments are conducted to test the accuracy and efficiency of the present method. The computed results indicate that the present scheme achieves the fourth-order accuracy and the effect of the multigrid method for accelerating the convergence speed is significant.

The cascadic multigrid method for elliptic problems

1996 ◽  
Vol 75 (2) ◽  
pp. 135-152 ◽  
Author(s):  
Folkmar A. Bornemann ◽  
Peter Deuflhard
Keyword(s):  
Multigrid Method ◽  
Elliptic Problems ◽  
Cascadic Multigrid ◽  
Cascadic Multigrid Method

scholarly journals SELF-CORRECTING MULTIGRID SOLVER

2006 ◽  
Vol 03 (02) ◽  
pp. 137-151
Author(s):  
JEROME L. V. LEWANDOWSKI
Keyword(s):  
Convergence Rate ◽  
Elliptic Problem ◽  
Short Wavelength ◽  
Multigrid Method ◽  
Source Term ◽  
Elliptic Problems ◽  
The Self ◽  
Multigrid Algorithm ◽  
Algebraic Error ◽  
Computational Work

A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It has shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.

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