Matrix properties
number of rows	1,157,456
number of columns	1,157,456
nonzeros	48,538,952
structural full rank?	yes
structural rank	1,157,456
# of blocks from dmperm	1
# strongly connected comp.	1
explicit zero entries	0
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
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 1157456-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	1,160,556,168
Cholesky flop count	4.8e+12
nnz(L+U), no partial pivoting, with AMD	2,319,954,880
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	2,693,105,368
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	6,428,054,924

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.