On the In uence of Partitioning Schemes on the E ciency ofOverlapping Domain Decomposition

One level overlapping Schwarz domain decomposition preconditioners can be viewed as a generalization of block Jacobi preconditioning. The eeect of the number of blocks and the amount of overlapping between blocks on the convergence rate is well understood. This paper considers the related issue of the eeect of the scheme used to partition the matrix into blocks on the convergence rate of the preconditioned iterative method. Numerical results for Laplace and linear elasticity problems in two and three dimensions are presented. The tentative conclusion is that using overlap tends to decrease the diierences between the rates of convergence for diierent partitioning schemes.