Optimal Injection Operator
in Multigrid Solution of the Three
Dimensional Poisson Equation
Jules Kouatchou and Jun Zhang
We present a multigrid solution of the three dimensional Poisson equation with a fourth-order 19-point finite difference scheme.
Using a red-black ordering of grid point and some geometric considerations, we derive an optimal scaled injection operator for the multigrid algorithm.
Numerical calculations show that this operator yields not only the smallest overall CPU time but also the best convergence rate compared to other more traditional projection operators.
In addition, we present a family of 19-point formulas and numerically show that each one has different optimal scaled injection operator.