@article{afba177a9f1744b1894ebfa0f2a4f1aa,

title = "Parallel implementation of efficient preconditioned linear solver for grid-based applications in chemical physics. I: Block Jacobi diagonalization",

abstract = "Linear systems in chemical physics often involve matrices with a certain sparse block structure. These can often be solved very effectively using iterative methods (sequence of matrix-vector products) in conjunction with a block Jacobi preconditioner [Numer. Linear Algebra Appl. 7 (2000) 715]. In a two-part series, we present an efficient parallel implementation, incorporating several additional refinements. The present study (paper I) emphasizes construction of the block Jacobi preconditioner matrices. This is achieved in a preprocessing step, performed prior to the subsequent iterative linear solve step, considered in a companion paper (paper II). Results indicate that the block Jacobi routines scale remarkably well on parallel computing platforms, and should remain effective over tens of thousands of nodes.",

keywords = "Block Jacobi, Chemical physics, Eigensolver, Linear solver, Parallel computing, Preconditioning, Sparse matrix",

author = "Wenwu Chen and Bill Poirier",

note = "Funding Information: This work was largely supported by the Office of Advanced Scientific Computing Research, Mathematical, Information, and Computational Sciences Division of the US Department of Energy under contract DE-FG03-02ER25534. Additional support from The Welch Foundation (D-1523) is also acknowledged. The authors wish to express special gratitude to Michael Minkoff and Albert F. Wagner, whose interest and motivation have made this work possible. Other researchers, notably Tucker Carrington, Jr., Stephen K. Gray, Dinesh K. Kaushik, Dmitry M. Medvedev, Ron Shepard, and Barry F. Smith, are also acknowledged for many stimulating discussions. In addition, we gratefully acknowledge use of “Jazz”, a 350-node computing cluster operated by the Mathematics and Computer Science Division at Argonne National Laboratory as part of its Laboratory Computing Resource Center. ",

year = "2006",

month = nov,

day = "20",

doi = "10.1016/j.jcp.2006.04.012",

language = "English",

volume = "219",

pages = "185--197",

journal = "Journal of Computational Physics",

issn = "0021-9991",

number = "1",

}