On improving the robustness and scalability of shared-memory AMG solvers for point-block problems

Abstract A number of modifications of the basic algorithms for constructing a multilevel structure to improve the performance of the algebraic multigrid method for both scalar and point-block systems are considered in this paper. We explore the basic operations of transposing and multiplying sparse matrices, as well as ways to select the maximum independent subset in the graph of strong connections, methods for constructing the prolongation operator, and approaches to aggressive coarsening that reduce the operation complexity of the method. It is shown that the construction of an extended prolongation operator can significantly increase the accuracy of the method, but at the cost of higher operator complexity and longer execution times. This disadvantage can be compensated either by filtering small weights from the prolongation operator, or by using aggressive coarsening. Several approaches to aggressive coarsening are considered. To confirm the conclusions, a number of numerical experiments were performed on a series of matrices from a publicly available collection for problems on progressively refined grids. The method applicability is evaluated on systems derived from adaptively generated grids. Some performance analisys of shared and hybrid memory is provided.