How to deal with domain's heterogeneity ?

[LPSavoie]

First of all, thank you so much for sharing py-pde and congratulations for such a beautiful code.
It is a shame though that this code doesn't seem capable of dealing with domain's heterogeneity ?

Problem statement:
Say we apply the diffusion equation div.(k.grad(T)=0 to a square domain of dimension 1 by 1
Boundary conditions are:
left hand side - Dirichlet / value= 1
right hand side - Dirichlet / value = 0
top and bottom sides - Neuman / derivative = 0

the domain is split in two:
0<= x <=0.5, k = 10
0.5< x <= 1, k = 1

Would py-pde allow the modeling of this simple example?

[david-zwicker]

This is certainly possible! In fact, there is an example, which solves a very similar problem.

[LPSavoie]

Thank you for the swift reply !
Indeed the example provides some heterogeneity in the domain, however the (1+tanh(x)) does not represent a strong / stiff discontinuity.
What about dealing with two very distinct domain properties?

[david-zwicker]

You could either make the hyperbolic tangent steeper, or you could also use a scalar field as the diffusivity via the consts Argument of the PDE class; see the documentation.