Matrix: Dziekonski/dielFilterV2real

Description: High-order vector finite element method in EM

Dziekonski/dielFilterV2real graph
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  • download as a MATLAB mat-file, file size: 384 MB. Use UFget(2386) or UFget('Dziekonski/dielFilterV2real') in MATLAB.
  • download in Matrix Market format, file size: 316 MB.
  • download in Rutherford/Boeing format, file size: 284 MB.

    Matrix properties
    number of rows1,157,456
    number of columns1,157,456
    structural full rank?yes
    structural rank1,157,456
    # of blocks from dmperm1
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetrysymmetric
    numeric value symmetrysymmetric
    Cholesky candidate?no
    positive definite?no

    authorA. Dziekonski, A. Lamecki, M. Mrozowski
    editorT. Davis
    kindelectromagnetics problem
    2D/3D problem?yes

    Additional fieldssize and type
    bfull 1157456-by-1


    High order vector finite element method in electromagnetics       
    The dielFilter* matrices came from analysis of a 4th-pole         
    dielectric resonator [4] generated with Finite Element Method.    
    The tetrahedral mesh of the structure was generated with the      
    Netgen mesher [2].  The matrices were used as an example in       
    our paper [3].                                                    
    dielFilterV2clx - complex symmetric matrix (607,232 x 607,232),   
        25,309,272 nonzero (real) and 728,900 nonzero (imag) elements.
        First 109,108 unknowns correspond to lowest level base        
    dielFilterV2real - real symmetric matrix (1,157,456 x 1,157,456)  
        and 48,538,952 nonzero elements.  First 209,432 unknowns      
        correspond to lowest level base functions.                    
    dielFilterV3clx - complex symmetric matrix (420,408 x 420,408),   
        32,886,208 nonzero (real) and 3,706,513 (imag) elements. First
        24,716 unknowns correspond to lowest level base functions,    
        next 116,152 unknowns correspond to the second level.         
    dielFilterV3real - real symmetric matrix (1,102,824 x 1,102,824)  
        and 89,306,020 nonzero elements. First 66,353 unknowns        
        correspond to lowest level base functions, next 305,729       
        unknowns correspond to the  second level.                     
    All matrices are sparse and come with right-hand-sides.           
    [2] J. Schoberl, "NETGEN An advancing front 2D/3D-mesh            
    generator based on abstract rules," Computing and Visualization   
    in Science, vol. 1, No. 1, pp.  41-52, July 1997                  
    [3] A. Dziekonski, A. Lamecki, M. Mrozowski, Tuning A             
    Hybrid GPU-CPU V-cycle Multilevel Preconditioner for Solving      
    Large Real and Complex Systems of FEM Equations.                  
    [4] F. Alessandri, M. Chiodetti, A. Giugliarelli; D. Maiarelli,   
    G. Martirano, D. Schmitt, L. Vanni and F. Vitulli.  The           
    electric-field Integral-equation method for the analysis and      
    design of a class of rectangular cavity filters loaded by         
    dielectric and metallic cylindrical pucks, Microwave Theory       
    and Techniques, IEEE Transactions on, vol. 52, no 8, pp.          
    1790-1797, Aug. 2004.                                             

    Ordering statistics:result
    nnz(chol(P*(A+A'+s*I)*P')) with AMD1,160,556,168
    Cholesky flop count4.8e+12
    nnz(L+U), no partial pivoting, with AMD2,319,954,880
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD2,693,105,368
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD6,428,054,924

    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.