FEM discretization of a viscoplastic collision problem, Alessio Quaglino
Name viscoplastic1
Group Quaglino
Matrix ID 1868
Num Rows 4,326
Num Cols 4,326
Nonzeros 61,166
Pattern Entries 61,166
Kind Materials Problem
Symmetric No
Date 2007
Author A. Quaglino
Editor T. Davis
Structural Rank 4,326
Structural Rank Full true
Num Dmperm Blocks 1
Strongly Connect Components 1
Num Explicit Zeros 0
Pattern Symmetry 74.1%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
SVD Statistics
Matrix Norm 7.387435e+01
Minimum Singular Value 5.290540e-04
Condition Number 1.396348e+05
Rank 4,326
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.