VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems

VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems

ARMS: an algebraic recursive multilevel solver for general sparse linear systems

This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into two subsets. The rst subset which can be termed \coarse" is obtained by using \block" independent sets, or \aggregates". Two aggregates have no coupling between them, but nodes in the same aggregate may be ...

pARMS: a parallel version of the algebraic recursive multilevel solver

A parallel version of the Algebraic Recursive Multilevel Solver (ARMS) is developed for distributed computing environments. The method adopts the general framework of distributed sparse matrices and relies on solving the resulting distributed Schur complement system. Numerical experiments are presented which compare these approaches on regularly and irregularly structured problems.

A parallel row projection solver for large sparse linear systems

In this paper we present a parallel iterative solver for large and sparse nonsymmetric linear systems. The solver is based on a row-projection algorithm, derived from the symmetrized block version of the Kacz-marz method with Conjugate Gradient acceleration. A comparison with some h'rylov subspace methods shows the remarkable robustness of this algorithm when applied to systems with eingevalues...

A distributed-memory hierarchical solver for general sparse linear systems

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direc...