3.6 PARAMETER FILE Z88I4.TXT FOR THE SPARSE MATRIX SOLVERS PART 2: Z88I2 AND Z88PAR

Mind the following formats:

[Long] = 4 bytes or 8 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 limit 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 ALPHA [Double].

This parameter for the SIC pre-conditioner of Z88I2 defines the Shift factor ALPHA (from 0 to 1, good values may vary from 0.0001 to 0.1. For further information consult the special literature)

4th entry: Convergence acceleration parameter OMEGA [Double].

This parameter for the SOR pre-conditioner of Z88I2 defines the Relaxation factor OMEGA (from 0 to 2, good values may vary from 0.8 to 1.2. How to choose OMEGA ? Good question! Try 1.0 for a first start and try other values for further Z88 runs with this structure.

5th entry: Z88PAR: number of cores or CPUs on multi-core computers. A maximum number of 9 is allowed.

Example 1: You want to stop after 5000 iterations, you choose a limit of 0.0000001 and the convergence acceleration parameter OMEGA will be 0.9 for use with SORCG solver.

> Thus: 5000 0.0000001 0.001 0.9 1

Example 2: You want to use the Sparse Matrix Iteration Solver Z88I2. You want to stop positively after 10000 iterations, the limit shall be 10-9 and the Shift factor ALPHA for SIC shall be 0.001 because you want to use the SIC pre-conditioner.

> Thus: 10000 1e-9 0.001 0.9 1

Example 3: You want to use the direct Sparse Matrix Solver with fill-in Z88PAR and you have two double core CPUs in your computer installed.

> Thus: 10000 1e-9 0.001 0.9 4

The not-underlined entries have no meaning for Z88PAR.