A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
MA57---a code for the solution of sparse symmetric definite and indefinite systems
ACM Transactions on Mathematical Software (TOMS)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
A parallel hybrid banded system solver: the SPIKE algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
A tearing-based hybrid parallel banded linear system solver
Journal of Computational and Applied Mathematics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Hi-index | 7.29 |
We propose a hybrid sparse system solver for handling linear systems using algebraic domain decomposition-based techniques. The solver consists of several stages. The first stage uses a reordering scheme that brings as many of the largest matrix elements as possible closest to the main diagonal. This is followed by partitioning the coefficient matrix into a set of overlapped diagonal blocks that contain most of the largest elements of the coefficient matrix. The only constraint here is to minimize the size of each overlap. Separating these blocks into independent linear systems with the constraint of matching the solution parts of neighboring blocks that correspond to the overlaps, we obtain a balance system. This balance system is not formed explicitly and has a size that is much smaller than the original system. Our novel solver requires only a one-time factorization of each diagonal block, and in each outer iteration, obtaining only the upper and lower tips of a solution vector where the size of each tip is equal to that of the individual overlap. This scheme proves to be scalable on clusters of nodes in which each node has a multicore architecture. Numerical experiments comparing the scalability of our solver with direct and preconditioned iterative methods are also presented.