Matrix: MaxPlanck/shallow_water1

Description: shallow water modelling, Max-Planck Inst. of Meteorology

MaxPlanck/shallow_water1 graph
(undirected graph drawing)


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  • Matrix group: MaxPlanck
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  • download as a MATLAB mat-file, file size: 2 MB. Use UFget(2261) or UFget('MaxPlanck/shallow_water1') in MATLAB.
  • download in Matrix Market format, file size: 3 MB.
  • download in Rutherford/Boeing format, file size: 2 MB.

    Matrix properties
    number of rows81,920
    number of columns81,920
    structural full rank?yes
    structural rank81,920
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?yes
    positive definite?yes

    authorK. Leppkes, U. Naumann
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes


    The two shallow_water* matrices arise from weather shallow water equations   
    (see, from the Max-Plank Institute of Meteorology. 
    The problem gives rise to an automatic differentiation problem.  An iterative
    solver is used for the larger problem, but a direct sovler is used for       
    finding the adjoints of a linear problem.  The velocity field is integrated  
    over a time loop with a semi-implicit method.  The implicit part leads to    
    a linear problem A*x=b, whose entries vary with time.  Two of these matrices 
    A are in this collection, with shallow_water1 at dtime=100 and shallow_water2
    at dtime=200.  The nonzero patterns of the two matrices are the same, but    
    shallow_water1 is much slower.  The reason is that many denormals appear     
    during factorization, which greatly slows down the BLAS.  This can be solved 
    by compiling with gcc -ffast-math, to flush denormals to zero.               

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD2,357,535
    Cholesky flop count5.8e+08
    nnz(L+U), no partial pivoting, with AMD4,633,150
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD5,355,578
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD9,691,968

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.