Reduced Domain Approximation Analysis about chimera HOT 2 OPEN

Using this approximation, I've observed convergence of ILUT preconditioned MCSA with 21 entries per row in the composite SPN operator, only 3 times as many as the original SPN operator, a big improvement over 2000 entries per row. This makes sense because if ILUT parameters were used to get a pretty good factorization, then those domain entries remaining after doing the approximation will therefore be the largest and have the greatest contribution to the Neumann series, effectively capturing most of the important pieces of the problem.

from chimera.

I've tested the reduced domain approximation with ParaSails preconditioning for SP1, 1-group problem 3. Here are the results with full weight recovery:

We note first that we can't reduce the fill level as low as we could with the ILUT preconditioning. ParaSails doesn't do as good of a job preconditioning in the first place so throwing away enough domain entries ultimately destroys convergence. The good news here is reducing the domain doesn't particularly reduce iterative performance when the method converges with an ideal fill level of 200 entries per row.

Now the weight recovery is set to 0:

This helps iterative performance a tremendous amount and now we can converge with a significantly reduced domain (at the cost of iterative performance). This is different than the initial ILUT observations where here zero weight recovery aids robustness. My thinking here is that the reduced domain from a more poorly conditioned problem (with ParaSails in this case), should not be pushed as hard in the Monte Carlo and hence reducing the size of the contributions to the estimator by reducing weights gives a similar effect to using a Neumann relaxation parameter of less than 1.

from chimera.