Matrix: Fluorem/RM07R

Description: RM07R: 3D viscous case with "frozen" turbulence. F. Pacull, Lyon, France

Fluorem/RM07R graph Fluorem/RM07R graph
(bipartite graph drawing) (graph drawing of A+A')

Fluorem/RM07R dmperm of Fluorem/RM07R

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  • download as a MATLAB mat-file, file size: 263 MB. Use UFget(2337) or UFget('Fluorem/RM07R') in MATLAB.
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  • download in Rutherford/Boeing format, file size: 350 MB.

    Matrix properties
    number of rows381,689
    number of columns381,689
    structural full rank?yes
    structural rank381,689
    # of blocks from dmperm109,055
    # strongly connected comp.109,055
    explicit zero entries0
    nonzero pattern symmetry 93%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorF. Pacull
    editorT. Davis
    kindcomputational fluid dynamics problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 381689-by-1
    xfull 381689-by-1


    CFD matrices from Francois Pacull, FLUOREM, in Lyon, France        
    We are dealing with CFD and more precisely steady flow             
    parametrization. The equations involved are the compressible       
    Navier-Stokes ones (RANS).  These matrices are real, square and    
    indefinite, they correspond to the Jacobian with respect the       
    conservative fluid variables of the discretized governing          
    equations (finite-volume discretization). Thus they have a         
    block structure (corresponding to the mesh nodes: the block        
    size is the number of variables per mesh node), they are not       
    symmetric (however, their blockwise structure has a high level     
    of symmetry) and they often show some kind of hyperbolic           
    behavior. They have not been scaled or reordered.                  
    They are generated through automatic differentiation of the        
    flow solver around a steady state. A right hand-side is also       
    given for each matrix: this represents the derivative of the       
    equations with respect to a parameter (of operation or shape).     
    Since they are generated automatically, they may have "silent"     
    variables: these are variables corresponding to an identity        
    submatrix associated with a null right hand-side, for example      
    one of the three velocity components in a 2D case, or the          
    turbulent variables in a "frozen" turbulence case.                 
    We believe that these matrices are good test cases when            
    studying preconditioning methods for iterative methods, such as    
    block incomplete factorization, or when studying domain            
    decomposition methods or deflation. They are actually being        
    studied by a few researchers in France regarding numerical         
    methods, through the LIBRAERO research project of the ANR (national
    research agency): ANR-07-TLOG-011.                                 
    Francois Pacull, Lyon, France.  fpacull at             
    Specific problem descriptions:                                     
        RM07R: 3D viscous case with "frozen" turbulence                
        number of mesh nodes: 54527                                    
        block size: 7                                                  
        variables: [rho,rho*u,rho*v,rho*w,rho*E,rho*k,rho*omega]       
        (rho k and rho omega are "silent", the sixth and seventh rows  
        and columns in each block can be removed)                      
        matrix order: 381689                                           
        nnz: 37464962                                                  
        comments: The geometry is a jet engine compressor.             

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD2,083,483,607
    Cholesky flop count3.4e+13
    nnz(L+U), no partial pivoting, with AMD4,166,585,525
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD2,045,670,467
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD3,709,383,659

    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.