What are the consequences of algebraic loops?

An algebraic loop is not a real problem in itself and does not prevent simulation capabilities. Simcenter Amesim will adapt to handle this type of modelling taking appropriate actions. As shown in the previous example, sorting out algebraic loops requires use of implicit numerical schemes and implicit formulation of equations. Many numerical procedures capable of sorting out this kind of problems exist, but these formulations can lower robustness of the numerical scheme.

• Implicit formulation can lead to singular or badly posed problems: there might be no real (or multiple) solution(s) (see examples provided previously). In these cases, singularity presented by a system of equations might cause problems for system solving.

• An implicit formulation requires usage of iterative processes that are traditionally based on Jacobian evaluations. Evaluating a Jacobian can be costly (mainly for large sized problems) and the global cost of model simulation in this case might increase in dramatic proportions.

• Numerical solvers used for implicit systems are generally driven by accuracy: they tend to ensure an accurate solution first, in order to avoid numerical drift that might violate error constraint in the following computations and thus ensure robustness rather than efficiency. This might result in slower computations than for the explicit case (although this is not always true).

In order to sort out algebraic loops, Simcenter Amesim introduces generated implicit variables that make it possible to switch to implicit formulation of the underlying system of equations, also introducing constraint equations defining the added unknown. Depending on the nature of the algebraic loop and number of variables exchanged in the flow of information, more than one generated implicit variable might be necessary to break the loop embedded in a system.