Matrix properties
number of rows	1,437,960
number of columns	1,437,960
nonzeros	60,236,322
structural full rank?	yes
structural rank	1,437,960
# of blocks from dmperm	66,481
# strongly connected comp.	66,481
explicit zero entries	2,920,368
nonzero pattern symmetry	symmetric
numeric value symmetry	symmetric
type	real
structure	symmetric
Cholesky candidate?	yes
positive definite?	yes

author	C. Janna, M. Ferronato
editor	T. Davis
date	2011
kind	structural problem
2D/3D problem?	yes

Notes:

Authors: Carlo Janna and Massimiliano Ferronato                 
                                                                
Symmetric Positive Definite Matrix                              
# equations:   1437960                                          
# non-zeroes: 63156690                                          
Problem description: Geomechanical problem                      
                                                                
The matrix Geo_1438 is obtained from a geomechanical problem    
discretizing a region of the earth crust subject to underground 
deformation. The computational domain is a box with an areal    
extent of 50 x 50 km and 10 km deep consisting of regularly     
shaped tetrahedral Finite Elements.  The problem arises from a  
3D discretization with three displacement unknowns associated to
each node of the grid.  This matrix has been used as a test case
in the following paper:                                         
                                                                
1) C. Janna, M. Ferronato, G. Gambolati. "A Block FSAI-ILU      
parallel preconditioner for symmetric positive definite linear  
systems". SIAM Journal on Scientific Computing, 32, pp.         
2468-2484, 2010.                                                

Ordering statistics:	result
nnz(chol(P*(A+A'+s*I)*P')) with AMD	6,297,700,169
Cholesky flop count	1.2e+14
nnz(L+U), no partial pivoting, with AMD	12,593,962,378
nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD	7,633,969,695
nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD	13,733,310,294

Note that all matrix statistics (except nonzero pattern symmetry) exclude the 2920368 explicit zero entries.

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.