Matrix: Quaglino/viscoplastic1

Description: FEM discretization of a viscoplastic collision problem, Alessio Quaglino

 (bipartite graph drawing) (graph drawing of A+A')

• Matrix group: Quaglino
• download as a MATLAB mat-file, file size: 3 MB. Use UFget(1868) or UFget('Quaglino/viscoplastic1') in MATLAB.

 Matrix properties number of rows 4,326 number of columns 4,326 nonzeros 61,166 structural full rank? yes structural rank 4,326 # of blocks from dmperm 1 # strongly connected comp. 1 explicit zero entries 0 nonzero pattern symmetry 74% numeric value symmetry 0% type real structure unsymmetric Cholesky candidate? no positive definite? no

 author A. Quaglino editor T. Davis date 2007 kind materials problem 2D/3D problem? yes

 Additional fields size and type b full 4326-by-1 C cell 7-by-1

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.
```

 Ordering statistics: result nnz(chol(P*(A+A'+s*I)*P')) with AMD 71,771 Cholesky flop count 2.2e+06 nnz(L+U), no partial pivoting, with AMD 139,216 nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD 705,015 nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD 1,530,390

 SVD-based statistics: norm(A) 73.8743 min(svd(A)) 0.000529054 cond(A) 139635 rank(A) 4,326 sprank(A)-rank(A) 0 null space dimension 0 full numerical rank? yes

 singular values (MAT file): click here SVD method used: s = piro_band_svd (A) status: ok