Quaglino/viscoplastic1
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 
5.290540e04 
Condition Number 
1.396348e+05

Rank 
4,326 
sprank(A)rank(A) 
0 
Null Space Dimension 
0 
Full Numerical Rank? 
yes 
Download Singular Values 
MATLAB

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Notes 
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.
