Parallel algorithms for the solution of narrow banded systems
Applied Numerical Mathematics
Parallel algorithms for banded linear systems
SIAM Journal on Scientific and Statistical Computing
Generalized Schwarz splittings
SIAM Journal on Scientific and Statistical Computing
Solving narrow banded systems on ensemble architectures
ACM Transactions on Mathematical Software (TOMS)
ScaLAPACK user's guide
On Stable Parallel Linear System Solvers
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
A parallel hybrid banded system solver: the SPIKE algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
On some parallel banded system solvers
Parallel Computing
A tearing-based hybrid parallel sparse linear system solver
Journal of Computational and Applied Mathematics
A numerical scheme for particle-laden thin film flow in two dimensions
Journal of Computational Physics
Hi-index | 7.30 |
A new parallel algorithm for the solution of banded linear systems is proposed. The scheme tears the coefficient matrix into several overlapped independent blocks in which the size of the overlap is equal to the system's bandwidth. A corresponding splitting of the right-hand side is also provided. The resulting independent, and smaller size, linear systems are solved under the constraint that the solutions corresponding to the overlap regions are identical. This results in a linear system whose size is proportional to the sum of the overlap regions which we refer to as the ''balance'' system. We propose a solution strategy that does not require obtaining this ''balance'' system explicitly. Once the balance system is solved, retrieving the rest of the solution can be realized with almost perfect parallelism. Our proposed algorithm is a hybrid scheme that combines direct and iterative methods for solving a single banded system of linear equations on parallel architectures. It has broad applications in finite-element analysis, particularly as a parallel solver of banded preconditioners that can be used in conjunction with outer Krylov iterative schemes.