Parallel multilevel iterative methods (Q5961589)

Solving a selfadjoint elliptic boundary value problem, the discretization results in a large scale system of linear equations. The system has a symmetric positive definite coefficient matrix with a block structure. The preconditioning matrices for such a system may be constructed using blocked multilevel iteration. The structure of the system and of preconditioning matrices suggest the application of parallel multilevel iterative techniques to solve the system using a multiprocessor computing system. NEWLINENEWLINENEWLINEThe authors propose a new class of such - strongly parallelized - methods and analyse their numerical and algorithmical properties: convergence rate, conditional numbers of the preconditioning matrices, computational work expenses and their dependence on the discretization and iteration parameters.