The influence of partitioning on Domain Decomposition convergence rates

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.