Under-Relaxation Algorithm

Under-relaxation is used to improve convergence of the overall analysis. It works by limiting a potentially large variation of the target-side data between two successive coupling iterations. For each data transfer location (node), the following formula is applied:

(5)

where

 

is the relaxed, target-side value.

 

is the reference target-side value. For coupling iterations within a coupling step, the reference target-side value is the final value from the last coupling iteration.

For the first iteration of the first step in a coupling run (either an initial or a restarted run), the reference target-side value is interpolated by System Coupling. For the first coupling iteration of all subsequent steps, the reference target-side value is the final value from the last coupling step.

 

is the raw, target-side value obtained from interpolation or from ramping (if applied).

Note that if you have applied both ramping and under-relaxation, the data are first ramped and then under-relaxed. In this case, for the under-relaxation's raw target-side value.

 

ω is the under-relaxation factor (URF). In a transient analysis, in the first coupling iteration of every coupling step, the URF is overridden and set to 1, and so data transferred at this coupling iteration is not under-relaxed.

For data model details, see RelaxationFactor in the System Coupling Settings and Commands Reference manual.