Abstract

This paper discusses the effects that partitioning has on the convergence rate of Domain Decomposition. When Finite Elements are employed to solve a second order elliptic partial differential equation with strong convection and/or anisotropic diffusion, the shape and alignment of a partition's parts significantly affect the Domain Decomposition convergence rate. Given a PDE, if $b$ is the direction of convection or the prominent direction of anisotropic diffusion, then if one considers traversing the domain in the direction of $b$, partitions having fewer parts to traverse in this direction converge faster while partitions having more converge slower.