3

3.6 PARAMETER FILE Z88I4.TXT FOR THE ITERATION SOLVER PART 2: Z88I2

Mind the following formats:

[Long] = 4 bytes integer number
[Double] = 8 bytes floating point number, alternatively with or without point

File only consists of only one line:

1st entry: Number of iterations MAXIT [Long]. When Z88I2 reaches this value, the solver is halted in any case. The results reached to this point are printed into Z88O2.TXT, however. This is the first halt criterion. Enter a value not too small e.g. 10000.

2nd entry: Limit EPS [Double]. This value is compared to a norm of the residual vector. When reaching this limit, the solution may have a good precision. This is the second halt criterion. Enter a relatively small value, e.g. 0.00001 or 0.0000001. This are quite proper and tested values. Note that there is no absolute truth in this field! Which ever norm of the residual vector is compared against the linit EPS - you can never be sure that all elements of the solution vector are precise. The choice of EPS has heavy influence on the iteration count and, thus, on the computing speed. Remember this when comparing Z88 to the big, commercial solvers (you don't really know which halt criterions these folks have programmed). The limits you may adjust in the commercial solvers may have nothing to do with EPS of Z88. However, many Z88- tests proved that the deflections of different nodes compared quite well to those from the commercial solvers if EPS was between 0.00001 and 0.0000001 with similar elapsed time. And pay attention to the fact, that you'll never know which solver delivers the best results when computing a large FEA structure!

3rd entry : Convergence acceleration parameter RP [Double]. Depends on your choice of preconditioner (the solver works with Conjugate Gradients, however).

- in case of SOR: Relaxation factor Omega (from 0 to 2, good values may vary from 0.8 to 1.2).
- in case of SIC: Shift factor Alpha (from 0 to 1, good values may vary from 0.0001 to 0.1). For further information consult the special literature)

I recommend SORCG (Conjugate Gradients with SOR preconditioning) as the default solver, because this solver needs only about 2/3 of memory of the second solver SICCG (shifted incomplete Cholesky decomposition, Conjugate Gradients). Which value may you choose for RP (reads here Omega) ? Good question ! Try RP with 1, this won't result in too bad results and vary RP for further runs with this FEA structure.

Example: You want to stop after 5000 iterations, you choose a limit of 0.00001and the convergence acceleration parameter will be 1 for use with SORCG solver.

> Thus: 5000 0.00001 1.