scholarly journals An H-Multigrid Method for Hybrid High-Order Discretizations

2021 ◽  
pp. S839-S861
Author(s):  
Daniele A. Di Pietro ◽  
Frank Hülsemann ◽  
Pierre Matalon ◽  
Paul Mycek ◽  
Ulrich Rüde ◽  
...  
Keyword(s):  
Multigrid Method ◽  
High Order

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.

scholarly journals A High-Order Compact (HOC) Implicit Difference Scheme and a Multigrid Method for Solving 3D Unsteady Reaction Diffusion Equations

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1208 ◽  
Author(s):  
Lili Wu ◽  
Xiufang Feng
Keyword(s):  
Difference Scheme ◽  
Fourth Order ◽  
Multigrid Method ◽  
Reaction Diffusion ◽  
High Order ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Implicit Difference Scheme ◽  
Euler Formula ◽  
Compact Difference

A high-order compact (HOC) implicit difference scheme is proposed for solving three-dimensional (3D) unsteady reaction diffusion equations. To discretize the spatial second-order derivatives, the fourth-order compact difference operators are used, and the third- and fourth-order derivative terms, which appear in the truncation error term, are also discretized by the compact difference method. For the temporal discretization, the multistep backward Euler formula is used to obtain the fourth-order accuracy, which matches the spatial accuracy order. To accelerate the traditional relaxation methods, a multigrid method is employed, and the computational efficiency is greatly improved. Numerical experiments are carried out to validate the accuracy and efficiency of the present method.

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