Matrix: Fluorem/DK01R

Description: DK01R: 1D turbulent case. F. Pacull, Lyon, France

Fluorem/DK01R graph Fluorem/DK01R graph
(bipartite graph drawing) (graph drawing of A+A')

Fluorem/DK01R dmperm of Fluorem/DK01R

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  • download as a MATLAB mat-file, file size: 89 KB. Use UFget(2334) or UFget('Fluorem/DK01R') in MATLAB.
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    Matrix properties
    number of rows903
    number of columns903
    structural full rank?yes
    structural rank903
    # of blocks from dmperm8
    # strongly connected comp.8
    explicit zero entries0
    nonzero pattern symmetry 96%
    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 903-by-1
    xfull 903-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:                                     
        DK01R: 1D turbulent case                                       
        number of mesh nodes: 129                                      
        block size: 7                                                  
        variables: [rho,rho*u,rho*v,rho*w,rho*E,rho*k,rho*omega]       
        (rho v and rho w are "silent", the third and fourth rows       
        and columns                                                    
        in each block can be removed)                                  
        matrix order: 903                                              
        nnz: 11758                                                     
        comments: The DK01R matrix corresponds to a small 1D turbulent 
        case. The grid has 129 nodes, non-uniformly spaced             
        (geometrical distribution). The number of unknowns per node is 
        7, leading to a linear system of 903 real algebraic equations. 
        The 1D discretization of the partial differential equations    
        uses a 5 points stencil, leading to a block penta-diagonal     
        matrix, each block having size 7 by 7. Each diagonal block is  
        related to two up- and two down-stream neighboring nodes,      
        corresponding respectively to the 14 upper and 14 lower matrix 
        rows, the node ordering being coherent with the 1D spatial     
        node distribution. The stationary flow on which the matrix is  
        based on is dominated by advection, characterized by a Mach    
        number around 0.3.                                             

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD7,807
    Cholesky flop count8.0e+04
    nnz(L+U), no partial pivoting, with AMD14,711
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD7,878
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD14,608

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    Fluorem/DK01R svd

    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.