FEM discretization of a viscoplastic collision problem, Alessio Quaglino
Name viscoplastic2
Group Quaglino
Matrix ID 1869
Num Rows 32,769
Num Cols 32,769
Nonzeros 381,326
Pattern Entries 381,326
Kind Materials Problem
Symmetric No
Date 2007
Author A. Quaglino
Editor T. Davis
Structural Rank 32,769
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 57%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
SVD Statistics
Matrix Norm 2.084753e+01
Minimum Singular Value 9.243401e-05
Condition Number 2.255396e+05
Rank 32,769
sprank(A)-rank(A) 0
Null Space Dimension 0
Full Numerical Rank? yes
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The matrix is in the form [A11 A12 ; A21 A22] where A11 and A22 are diagonal. 
Originally, the matrices in this set were poorly scaled, but this was resolved
by a scale factor of the form [A11 A12*e ; A21/e A4] where the scalar e is    
of magnitude 1e2 but can be 1e6 or 1e7 for a stiff material.  The Problem.A   
matrix is the properly scaled problem.  The Problem.aux.C{1:7} matrices have  
been "unscaled" with a factor e = 10.^(-(1:7)), to give a sequence of matrices
that are well scaled to poorly scaled, and thus well conditioned (C{1}) to    
poorly conditioned (C{7}).  This mimics the original poorly scaled and ill-   
conditioned problem, and may be of interest for those developing algorithms   
for automatic scaling.  From a FEM discretization of a viscoplastic collision 
problem, Alessio Quaglino.