A Two Colorable Fourth Order Compact Difference
Scheme and Parallel Iterative Solution of
the 3D Convection Diffusion Equation
Jun Zhang and Lixin Ge
Department of Computer Science
University of Kentucky
773 Anderson Hall
Lexington, KY 40506-0046, USA
NASA Goddard Space Flight Center - Code 931
Greenbelt, MD 20771, USA
A new fourth order compact difference scheme for the three dimensional
convection diffusion equation with variable coefficients is presented.
The novelty of this new difference scheme is that it only requires
15 grid points and that it can be decoupled with two colors. The entire
computational grid can be updated in two
parallel subsweeps with a Gauss-Seidel type
iterative method. This is compared with the known 19 point fourth
order compact difference scheme which requires four colors to decouple the
computational grid. Numerical results, with multigrid methods implemented
on a shared memory parallel computer, are
presented to compare the 15 point and 19 point fourth
order compact schemes.
Key words: 3D convection diffusion equation,
fourth order compact difference schemes, multigrid method,
Mathematics Subject Classification: 65M06, 65N12.
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This paper has been published in
Mathematics and Computers in Simulation, Vol. 54, (1-3)m 67-83,
2000. Technical Report No. 301-00, Department of Computer Science,
University of Kentucky, Lexington, KY, 2000.
This research of the first two authors was supported in part
by the U.S. National Science Foundation under the grant
CCR-9902022, and in part by the University of Kentucky
Center for Computational Sciences.
This third author is also affiliated with Morgan State University and his
research was supported by NASA under the grant No. NAGS-3508.