Fluide mechanics matrices from Ralph Goodwin, Univ. Illinois.
The goodwin.rua matrix:
A finite-element matrix from Ralph Goodwin, Chemical Engineering Dept.,
Univ. of Illinois at Urbana-Champaign. A fluid mechanics problem.
From a nonlinear solver (Newton iterations. Uses several back
substitutions for the Sherman-Morrison formula to deal with a dense
row (not given in the matrix).
The matrix was originally obtained in triplet (i,j,a_ij) format, with
lots of duplicate entries (from unassembled finite elements).
Converted (and duplicates assembled) into RUA format by Tim Davis.
email: ralph :at the domain: wsnext.scs.uiuc.edu
The rim.rua matrix: n=22560, nz=1014951. Originally in triplet format with
duplicate entries. See comments below:
From ralph :at the domain: wsnext.scs.uiuc.edu Mon May 22 16:31:26 1995
Tim,
I have another matrix that may interest you. It is similar
to the matrix that you added to the Boeing-Harwell library.
THere are 22560 equations. The frontwidth is about 144.
However pivoting consideration cause the frontwidth to grow
to 2174. I have not tried using UMFPACK with this matrix
because my code requires 287 Mbytes to store the LU factors,
and therefore goes out-of-core. Still if you are
interested in a matrix that appears to have severe pivoting
problems and is big then I have one for you.
Ralph Goodwin
From ralph :at the domain: wsnext Fri May 26 08:03:45 1995
Tim,
I solved my problem of excessive front width growth by rescaling
the rows of the matrix, so I guess I sounded a false alarm.
Previously, the front would grow from 155 to 2300, now it stays
at 144. I rescaled by the 1 norm of each row.
Ralph
From ralph :at the domain: wsnext.scs.uiuc.edu Fri May 26 14:27:21 1995
Tim,
I ftped the matrix to you. It is in the
directory incoming and is named rim.mat.gz. It is
a 15Mb file that uncompresses to about 42Mb. The matrix
is stored in triple format with the first two lines
being the order of the matrix and the number of nonzeroes.
There are duplicate nonzeroes that must be summed.
Earlier I said that I scaled the rows by their 1 norm.
This is not exactly correct. I scaled by the 1 norm
of the *unsummed* nonzeroes in the row, which is of
course different than the 1 norm of the row.
Ralph
From ralph :at the domain: wsnext.scs.uiuc.edu Fri May 26 14:53:18 1995
Yes, it is from the same application. The physical properties
are different (viscosity, density, ...) but otherwise it is
the same problem. One more thing about this problem is that
it involves not only solving the steady Navier-Stokes (N-S) equations
but also solving a pair of elliptic mesh generation (EMG) equations.
The EMG equations are coupled to the N-S equations by
boundary conditions. So the system of equations represented
by the matrix I sent you (and also goodwin.rua) is both
N-S equations and EMG equations all discretized using quadrilateral
biquadratic finite elements. The main point is that the matrix
is not just a discretization of the N-S equations.
Ralph
Minor change, 3/31/03: "rua" changed to "RUA", in rim.rua header.