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3.2.4 Limiting Values

Each quantity can also be limited to certain bounds. For instance an impurity is known to be positive because of physical restrictions and therefore a minimum limit of zero can be set. This sometimes results in a higher convergence rate due to the fact, that erroneous calculations during Newton iterations are cut off. But sometimes this strict limitation reduces the convergence or even prevents the system from converging. Furthermore, the user has to be careful because although such adjustments can be used to meet physical properties (e.g. positivity of concentrations), application of these can violate other physical properties (e.g. conservation of matter).

MinLimit(<QuantityName>) = <minimum limit value>
MaxLimit(<QuantityName>) = <maximum limit value>

Finally a separate epsilon value can be assigned to each quantity as a limiting value for the Newton iterations that calculates the error of the system using an $ L_2$ norm. With this mechanism the number of Newton iterations for quantities of less importance or accuracy can be reduced accepting a higher error of the result:

Epsilon(<QuantityName>) = <value>



M. Radi, E.Leitner, and S. Selberherr