Matrix properties
number of rows	607,232
number of columns	607,232
nonzeros	25,309,272
structural full rank?	yes
structural rank	607,232
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	97%
type	complex
structure	symmetric
Cholesky candidate?	no
positive definite?	no

author	A. Dziekonski, A. Lamecki, M. Mrozowski
editor	T. Davis
date	2011
kind	electromagnetics problem
2D/3D problem?	yes

Additional fields	size and type
b	full 607232-by-1

Notes:

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        
    functions.                                                    
                                                                  
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 AMD	426,850,000
Cholesky flop count	1.3e+12
nnz(L+U), no partial pivoting, with AMD	853,092,768
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	1,187,745,302
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	2,848,515,948

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.