Comparison of some domain decomposition algorithms for nonsymmetric elliptic problems

In recent years, competitive domain-decomposed preconditioned iterative techniques have been developed for nonsymmetric elliptic problems. In these techniques, a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow effective solution on parallel machines. Central questions are how to choose these small problems and how to arrange the order of their solution. Different specifications of decomposition and solution order lead to a plethora of algorithms possessing complementary advantages and disadvantages. In this report we compare several methods, including the additive Schwarz algorithm, the multiplicative Schwarz algorithm, the tile algorithm, the CGK and CSPD algorithms, and the popular global ILU-family of preconditioners, on some nonsymmetric and/or indefinite elliptic model problems discretized by finite difference methods. The preconditioned problems are solved by the unrestarted GMRES method.