Matrix: Fluorem/HV15R

Description: HV15R: 3D engine fan. F. Pacull, Lyon, France

Fluorem/HV15R graph Fluorem/HV15R graph
(bipartite graph drawing) (graph drawing of A+A')

Fluorem/HV15R dmperm of Fluorem/HV15R

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  • download as a MATLAB mat-file, file size: 2029 MB. Use UFget(2384) or UFget('Fluorem/HV15R') in MATLAB.
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    Matrix properties
    number of rows2,017,169
    number of columns2,017,169
    structural full rank?yes
    structural rank2,017,169
    # of blocks from dmperm24,683
    # strongly connected comp.24,683
    explicit zero entries0
    nonzero pattern symmetry 84%
    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 2017169-by-1
    xfull 2017169-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:                                     
       This is a 3D Reynolds-Averaged-Navier-Stokes case.              
       HV15R: 3D engine fan. The flow has a low Mach number.           
       Number of mesh nodes: 288,167                                   
       block size: 7                                                   
       variables: [rho, rho*u, rho*v, rho*w, rho*E, rho*k, rho*omega]  
       matrix order: 2,017,169                                         
       nnz: 283,073,458                                                
    In 2011, this problem took 3.5 hours to solve, using GMRES with    
    an adaptive Schwarz preconditioner and ILU withing the subdomains, 
    requiring about 100GB of memory.                                   
    Reference:  "A Study of ILU Factorization for Schwartz             
    Preconditioners with Application to Computational Fluid            
    Dynamics", F. Pacull, S. Aubert, M. Buisson, Proceedings           
    of the 2nd Intl Conf on Parallel, Distributed, Grid, and           
    Cloud Computing for Engineering, B.H.V Topping and P.              
    Iva'nyi, Editors.  Civil-Comp Press, Stirlingshire,                
    Scotland, 2011.                                                    

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD52,974,483,341
    Cholesky flop count3.3e+15
    nnz(L+U), no partial pivoting, with AMD105,946,949,513
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD54,682,928,546
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD98,098,157,490

    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.