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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.