A Two Colorable Fourth Order Compact Difference Scheme and Parallel
Iterative Solution of the 3D Convection Diffusion Equation
Jun Zhang, Lixin Ge and Jules Kouatchou
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.