Stretched and Filtered Transport Precondititioning of Sn Problems Part 2: Heterogeneous Media

Hanshaw, H L ; Nowak, P ; Larsen, E W

Lawrence Livermore National Laboratory

关键词: Acceleration;    Breakdown;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Eigenvalues;    Transport;   

DOI  :  10.2172/15005883
RP-ID  :  UCRL-JC-153706-2
RP-ID  :  W-7405-ENG-48
RP-ID  :  15005883

美国|英语

来源: UNT Digital Library

【 摘 要 】

In [1], we presented the stretched filtered transport synthetic acceleration method (SFTSA) for homogeneous media. Both SFTSA and SFTSA preconditioned Krylov were shown to be effective iterative schemes in homogeneous media due to the predictable structure of the iteration eigenvalues. In heterogeneous media or on non-uniform grids, the eigenvalue structure is unpredictable for general problems, making the filter strength a for optimal SFTSA extremely problem dependent. Leaving Q set to the optimal value (in each cell by table lookup) predicted by homogeneous media theory can make SFTSA divergent, even for relatively mild heterogeneities. Thus, SFTSA is more fragile than DSA in the sense that most DSA schemes break down only for much more severe heterogeneities. Fortunately, breakdown of SFTSA occurs with large negative eigenvalues, and Krylov methods preconditioned with SFTSA remain effective for such problems. Therefore, with a Krylov scheme ''wrapped around'' SFTSA, the resulting method is relatively insensitive to the filter strength, and a user may achieve reasonably good performance, if not optimal, with a fixed a over a wide range of heterogeneous problems.