The simplest algebraic loop possible within Simcenter Amesim

The simplest algebraic loop that can be built in Simcenter Amesim is the following one.

Figure 52: Simplest algebraic loop

Let’s denote x (resp. y) the input (resp. output) of the FX00 submodel. The direct line between the ouptput and input of tthe FX00 submodel ensures equality of the x and y values.

At a given time the equation governing values of y is given by:

The solution of this equation might be a fixed point of function (if it exists).

For example,

• Specifying , the problem is singular, owning an infinite number of solutions.

• Specifying , the problem has a unique solution in [0;+∞[.

• Specifying , the problem has a unique solution in [0;+∞[.

• Specifying , the problem does not have any solution in [0;+∞[.

• Specifying , the problem has two solutions in ]-∞;+∞[. In this case the "nearest" one is computed by Simcenter Amesim.

In some cases, the equations can even easily be simplified and y value can directly be expressed as an algebraic or numerical expression. But in common cases, f is a nonlinear expression (as in 3 last previous examples) and there is no direct way to compute the root of these expressions. In scientific computing, solving these equations requires an implicit process, called fixed point iteration.