High-Order Multigrid Techniques
for
Partial Differential Equations
Jules Kouatchou
We examine the effect of combining high-order compact finite difference approximations and multigrid procedures to solve partial differential equations.
High-order multigrid performance is analytically and numerically analyzed to show that the method is stable and produces solution with high accuracy.
We introduce in the multigrid algorithm a scaled injection as projection operator that renders the implementation efficient and less computational expensive than other projection operators.
The scaled injection operator is employed not only to recover convergence when standard methods fail but also as an accelaration technique of the algorithm.
Our analysis is mainly based on two and three dimensional Poisson and convection-diffusion equations.