This demonstration shows a combination of:

1) Finite element analysis (FEA) of solid body heat transfer with non-linear material properties
2) Optimisation of an output of the FEA

specifically related to a real world problem. We walk through the general process, which is:

1) Generate a representative FEA solver wrapped into a function
2) Use Surrogate Optimisation to find a close, but fast, approximation of the global optimum
3) Deploy a local solver based on the output of the Surrogate Optimisation to polish and find the global optimum

We will look at the case of a current carrying conductor that is buried underground. In this case we want to maximise the current that can be carried subject to the insulator staying below a fixed temperature.