Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Parallel Tridiagonal Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Implementation in ScaLAPACK of Divide-and-Conquer Algorithms forBanded and Tridiagonal Linear Systems
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Using OpenMP: Portable Shared Memory Parallel Programming (Scientific and Engineering Computation)
Towards high performance discrete-event simulations of smart electric grids
Proceedings of the first international workshop on High performance computing, networking and analytics for the power grid
Journal of Parallel and Distributed Computing
Journal of Parallel and Distributed Computing
| Hi-index | 31.45 |
A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algorithm that is easily parallelized. Storage of the factored blocks allows the application of the inverse to multiple right-hand sides which may not be known at factorization time. Scalability with the number of block rows is achieved with cyclic reduction, while scalability with the block size is achieved using multithreaded routines (OpenMP, GotoBLAS) for block matrix manipulation. This dual scalability is a noteworthy feature of this new solver, as well as its ability to efficiently handle arbitrary (non-powers-of-2) block row and processor numbers. Comparison with a state-of-the art parallel sparse solver is presented. It is expected that this new solver will allow many physical applications to optimally use the parallel resources on current supercomputers. Example usage of the solver in magneto-hydrodynamic (MHD), three-dimensional equilibrium solvers for high-temperature fusion plasmas is cited.