A comparison of some domain decomposition and ILU preconditioned iterative methods for nonsymmetric elliptic problems

In recent years competitive domain decomposed preconditioned iterative tech niques have been developed for nonsymmetric elliptic problems In these tech niques a large problem is divided into many smaller problems whose requirements for coordination can be controlled to allow e ective solution on parallel machines A central question is how to choose these small problems and how to arrange the order of their solution Di erent speci cations of decomposition and solution or der lead to a plethora of algorithms possessing complementary advantages and disadvantages In this report we compare several methods including the additive Schwarz algorithm the classical multiplicative Schwarz algorithm an acceler ated multiplicative Schwarz algorithm the tile algorithm the CGK algorithm the CSPD algorithm and also the popular global ILU family of preconditioners on some nonsymmetric or inde nite elliptic model problems discretized by nite di erence methods The preconditioned problems are solved by the unrestarted GMRES method A version of the accelerated multiplicative Schwarz method is a consistently good performer