Optimal Interface Conditions for Domain Decomposition Methods

We define optimal interface conditions for the additive Schwarz method (ASM) in the sense that convergence is achieved in a number of steps equals to the number of subdomains. Since these boundary conditions are difficult to use, we approximate them by partial differential operators that are easier to use. We present numerical results using these approximate interface conditions for the ASM and Schur type methods (substructuring). We also give a new result of convergence for BiCG which is then used for BiCGSTAB.