A Bit-Compatible Parallelization for ILU(k) Preconditioning

  • Xin Dong
  • Gene Cooperman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6853)


ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that maintains this important stability property. Even better, TPILU(k) preconditioning produces an answer that is bit-compatible with the sequential ILU(k) preconditioning. In terms of performance, the TPILU(k) preconditioning is shown to run faster whenever more cores are made available to it — while continuing to be as stable as sequential ILU(k). This is in contrast to some competing methods that may become unstable if the degree of thread parallelism is raised too far. Where Block Jacobi ILU(k) fails in an application, it can be replaced by TPILU(k) in order to maintain good performance, while also achieving full stability. As a further optimization, TPILU(k) offers an optional level-based incomplete inverse method as a fast approximation for the original ILU(k) preconditioned matrix. Although this enhancement is not bit-compatible with classical ILU(k), it is bit-compatible with the output from the single-threaded version of the same algorithm. In experiments on a 16-core computer, the enhanced TPILU(k)-based iterative linear solver performed up to 9 times faster. As we approach an era of many-core computing, the ability to efficiently take advantage of many cores will become ever more important.


Domain Decomposition Gaussian Elimination Iterative Solver Sparse Linear System Preconditioned Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Xin Dong
    • 1
  • Gene Cooperman
    • 1
  1. 1.College of Computer ScienceNortheastern UniversityBostonUSA

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