Table of Contents
Solver control parameters for a steady-state nonlinear problem
The XT2S/XT3S solver control parameters are specified in the name.iB file:
IP 1 0 KOUT 0 NSAX NSTEPX 1 RP 0 ERAL EDIF 0 0 PIVOT PENAL
KOUT is the log output key:
$=1$ … sequence of all approximations
$=2$ … solution only
NSAX is the maximum number of successive approximations before performing a new matrix factorization. The recommended value is $10<\mathtt{NSAX}<20$.
NSTEPX: If $\mathtt{NSTEPX}<0$, the line search acceleration is not used.
ERAL is the residual convergence criterion. The recommended value is $10^{-5}<\mathtt{ERAL}<10^{-2}$. It applies only when $\mathtt{KAPPR}=1$.
EDIF is the convergence criterion for the temperature increment $[^\circ\text{C}]$. The recommended value is $1<\mathtt{EDIF}<10$. It applies only when $\mathtt{KAPPR}=1$.
PIVOT is the minimum allowed pivot value during matrix factorization. The default value is $10^{-6}$.
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 $\mathtt{KAPPR}=1$:
AV 1 T 6 N 1 0 0 V 4*0
by assigning it in the AS batch:
AS load case number /$\dots$ /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.
Commentary
For a nonlinear problem, it is necessary to express all quantities (boundary conditions and material properties) in terms of the resulting nodal temperatures, which are, however, 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 temperature change in two consecutive iterations, and simultaneously a small residual magnitude, 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 a 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 set 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 (AV set with $\mathtt{KAPPR}=1$), it is necessary to specify the initial approximation of the temperature field using a GV set.