Solver control parameters for steady-state nonlinear analysis
The control parameters of the XT2S/XT3S solver are specified in the name.iB file:
IP 1 0 KOUT 0 NSAX NSTEPX 1 RP 0 ERAL EDIF 0 0 PIVOT PENAL
$\mathtt{KOUT}$ is the report output key:
$=1$ … sequence of all approximations
$=2$ … solution only
$\mathtt{NSAX}$ is the maximum number of successive approximations before initiating a new matrix factorization. The recommended value is $10<\mathtt{NSAX}<20$.
If $\mathtt{NSTEPX}<0$, the line search acceleration is not used.
$\mathtt{ERAL}$ is the convergence criterion for the residual. The recommended value is $10^{-5}<\mathtt{ERAL}<10^{-2}$. It applies only when $\mathtt{KAPPR}=1$.
$\mathtt{EDIF}$ $[^\circ\text{C}]$ is the convergence criterion for the temperature increment. The recommended value is $1<\mathtt{EDIF}<10$. It applies only when $\mathtt{KAPPR}=1$.
$\mathtt{PIVOT}$ is the minimum allowed pivot value during matrix factorization. The default value is $10^{-6}$.
$\mathtt{PENAL}$ is the penalty function value for connector elements of all types. The default value is $10^6$.
The assignment /R TIMX STEP TSC/ in the AS batch is not used.
However, it is recommended to activate the AV set with the key $\mathtt{KAPPR}=1$:
AV 1 T 6 N 1 0 0 V 4*0
by assigning it in the AS batch:
AS load case index /$\dots$ /A 1 /$\dots$
Each load case corresponds to a single record containing a steady-state temperature field in both the name.TEM and name.STR files.
Considerations
For a nonlinear problem, it is necessary to express all quantities (boundary conditions and material properties) for the resulting nodal temperatures, which, however, are not known in advance. For this reason, the solution is corrected using a modified or, where applicable, accelerated ($\mathtt{NSTEPX}\ge0$) Newton-Raphson method. The convergence criterion is a small change in temperatures in two consecutive iterations, and simultaneously the magnitude of the residual, i.e., $$\begin{array}{lll} \max|\mathbf{T}^{(i+1)}-\mathbf{T}^{(i)}| < \mathtt{EDIF} & \land & ||\operatorname{Res}\mathbf{T}^{(i)}|| < \mathtt{ERAL}\,||\mathbf{T}^{(i)}||. \end{array}$$
If convergence is slow, a new system matrix can be assembled for the current temperature approximation. However, this procedure requires new factorization, which is very time-consuming. The $\mathtt{NSAX}$ parameter determines the number of successive approximations after which a new system matrix is formed, if convergence has not yet been achieved.
An important parameter is the $\mathtt{KAPPR}$ key, which initiates the solution correction process. If $\mathtt{KAPPR}=0$ or if the AV batch is missing (has not been assigned), the convergence check is not performed, and the calculation terminates after the first iteration. This results in a steady-state linear solution with quantities expressed for the initial temperature.
The convergence progress can be monitored using the $\mathtt{KOUT}$ key. If only the results are required, $\mathtt{KOUT}=2$ is set.
Note
When using the iterative method (AVset with $\mathtt{KAPPR}=1$), it is necessary to specify the initial approximation of the temperature field using theGVset.
