Squashed ball

[dsrawlins]

This is the example I used to compare the linear solvers SuperLU and Skyline. It consists of a flat, stiff box pushing down on a softer ball (both Mooney-Rivlin) with a sliding contact between them. Note that it was important to removed all symmetry from the problem. It was run on an AMD Athelon 64 dual core with 2G memory.

Number of equations: 51,014

Results:

Skyline:

Average memory usage: 1G
Time in solver: 5 hrs 15 min 25 sec

SuperLU:

Average memory usage: 1.6G
Time in solver: 7 hrs 34 min 14 sec

Conclusions:

Although there was contact in the problem, the stiffness matrix was still simple enough that Skyline out-performed SuperLU. See Steve Maas' contact problem for an example where SuperLU did better than Skyline.

[weiss]

Probably worth mentioning that SuperLU is not a symmetric solver. Thus it will generally use more memory and require many more floating point operations than a solver that takes advantage of the symmetry in the matrix. Hopefully it will perform well once we test it with mulitple processors (SMP).

Cheers,

Jeff

[maas]

I think in general it can be expected that for sufficiently complex problems the SuperLU solver (SLU) will perform better. The main difference between the SLU solver and the default Skyline solver is the storage scheme for the sparse stiffness matrix. SLU uses a more efficient method to store the nonzero members of the matrix and is less dependant on the bandwidth of the matrix, although (as Jeff already pointed out) it does store the entire matrix, where Skyline only stores half of it. As a rule of thumb, for the following problems it is expected (but not guaranteed) that SLU will perform better than Skyline:

-non-regular meshes without bandwidth optimization
-contact problems with large sliding

We will be continuing to test the SLU (and other) solvers. We also encourage our users to test the different solvers on their models and to post their findings on the forum.

Cheers,

Steve.