On the performance of SPAI and ADI-like preconditioners for core collapse supernova simulations in one spatial dimension

Dennis C. Smolarski, Ramesh Balakrishnan, Eduardo F. D'Azevedo, John W. Fettig, Bronson Messer, Anthony Mezzacappa, Faisal Saied, Paul E. Saylor, F. Douglas Swesty

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The simulation of core collapse supernovæ calls for the time accurate solution of the (Euler) equations for inviscid hydrodynamics coupled with the equations for neutrino transport. The time evolution is carried out by evolving the Euler equations explicitly and the neutrino transport equations implicitly. Neutrino transport is modeled by the multi-group Boltzmann transport (MGBT) and the multi-group flux limited diffusion (MGFLD) equations. An implicit time stepping scheme for the MGBT and MGFLD equations yields Jacobian systems that necessitate scaling and preconditioning. Two types of preconditioners, namely, a sparse approximate inverse (SPAI) preconditioner and a preconditioner based on the alternating direction implicit iteration (ADI-like) have been found to be effective for the MGFLD and MGBT formulations. This paper compares these two preconditioners. The ADI-like preconditioner performs well with both MGBT and MGFLD systems. For the MGBT system tested, the SPAI preconditioner did not give competitive results. However, since the MGBT system in our experiments had a high condition number before scaling and since we used a sequential platform, care must be taken in evaluating these results.

    Original languageEnglish
    Pages (from-to)330-338
    Number of pages9
    JournalComputer Physics Communications
    Volume175
    Issue number5
    DOIs
    StatePublished - Sep 1 2006

    Funding

    This work is supported by the Department of Energy SciDAC cooperative agreement DE-FC02-01ER41185, http://www.phy.ornl.gov/tsi/ . This research work used the computational resources at the National Center for Supercomputing Applications, http://www.ncsa.uiuc.edu .

    FundersFunder number
    U.S. Department of EnergyDE-FC02-01ER41185
    U.S. Department of Energy

      Keywords

      • Finite-difference methods
      • Multi-group Boltzmann equation
      • Multi-group flux limited diffusion
      • Numerical simulation
      • Preconditioners
      • Radiative transfer
      • Solution of equations
      • Supernovæ

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