ISSN:
0271-2091
Keywords:
Multigrid
;
Iterative Improvement
;
Geothermal Model
;
Alternating-direction-implicit
;
Tau-extrapolation
;
Higher-order-accuracy
;
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
This paper considers the multigrid iterative method applied to the solution of finite difference approximations to a linear second-order self-adjoint elliptic equation. It represents an extension of work by Dinar and Brandt. We compare two methods to obtain fourth-order convergence. The first is local error extrapolation developed by Brandt, the second is iterative improvement developed by Lindberg. This work considers non-separable problems, but only on a rectangular domain with Dirichlet boundary conditions. We consider test cases with non-smooth (i.e. discontinuous second derivatives) as well as smooth solutions. We also apply the multigrid method to an elliptic equation with non-separable coefficients which occurs in a geothermal model. In this case an analysis of the error fails to show any advantage in a fourth-order difference scheme over a second-order scheme. However, we do demonstrate that the multigrid iteration performs well on this problem. Also, this example shows that the multigrid iteration can be combined with iterative improvement to create an efficient fourth-order method for a non-separable elliptic equation which is coupled with a marching equation. Other work has found an advantage in this fourth-order scheme for a similar geothermal model.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/fld.1650020104
