Matrix: Fluorem/GT01R

Description: GT01R: 2D inviscid case. F. Pacull, Lyon, France

Fluorem/GT01R graph Fluorem/GT01R graph
(bipartite graph drawing) (graph drawing of A+A')

Fluorem/GT01R dmperm of Fluorem/GT01R

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  • download as a MATLAB mat-file, file size: 3 MB. Use UFget(2335) or UFget('Fluorem/GT01R') in MATLAB.
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    Matrix properties
    number of rows7,980
    number of columns7,980
    structural full rank?yes
    structural rank7,980
    # of blocks from dmperm4
    # strongly connected comp.4
    explicit zero entries0
    nonzero pattern symmetry 88%
    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 7980-by-1
    xfull 7980-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:                                     
        GT01R: 2D inviscid case                                        
        number of mesh nodes: 1596                                     
        block size: 5                                                  
        variables: [rho,rho*u,rho*v,rho*w,rho*E]                       
        (rho w is "silent", the fourth row and column in each          
        block can be removed)                                          
        matrix order: 7980                                             
        nnz: 430909                                                    
        comments: This is a 2D linear cascade turbine case. The grid   
        corresponds to one inter-blade channel. The stencil involved   
        by the convective scheme uses 9 nodes. Thus, there are 9       
        non-zero blocks for each node in the matrix. The specificity   
        is that the computational domain is periodic, which introduces 
        some non-zeros elements far away from the diagonal.            

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD1,446,641
    Cholesky flop count3.3e+08
    nnz(L+U), no partial pivoting, with AMD2,885,302
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD2,765,274
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD5,518,657

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

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

    Fluorem/GT01R 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.