How does homotopy operator work?

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Joined: 2017-07-04
How does homotopy operator work?


i want to use homotopy to solve a system of nonlinear equations during the initialization phase of a dynamic simulation problem.

The general structure looks like this: z = homotopy(actual = z_0 , simpliefied = z_ref). I am not sure, if i completely understand how it works.

First i tried to use it in an initial equation, but it doesn't work really good.

So i have two questions:

1) if i use it as a normal equation instead of initial equation, does the homotopy interate the dynamic state of the system the hole time or just at the beginning?

2) On wich state should i refer the other variables at the initialization? On the simpliefied or the actual state?


Thanks for your support