BCYCLIC: A Paralell Block Tridiagonal Matrix Cyclic Solver Articles uri icon

publication date

  • February 2010

start page

  • 6392

end page

  • 6404


  • 18


  • 229

International Standard Serial Number (ISSN)

  • 0021-9991

Electronic International Standard Serial Number (EISSN)

  • 1090-2716


  • A block tridiagonal matrix is factored with minimal fill-in using a cyclic reduction algo- rithm 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 scalabil- ity 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 pro- cessor 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 mag-
    neto-hydrodynamic (MHD), three-dimensional equilibrium solvers for
    high-temperature fusion plasmas is cited.