Solve PDE with min

[lmanda7]

Hi, I am working on solving the following spatial PDE for $h(x): \mathbb{R}^2\rightarrow \mathbb{R}$
$$\min\{c(x) - h(x),\; x_2\frac{\partial}{\partial x_1}h(x) + |\frac{\partial}{\partial x_2}h(x)| + \gamma h(x)\} = 0, \; \forall x\in \mathcal{X}$$
where $c(x)$ is a known input function which can be precomputed on the mesh, $\mathcal{X}=[l_{x_1}, u_{x_1}]\times[l_{x_2}, u_{x_2}]$ is the rectangular domain of interest, and $\gamma\geq 0$ is a constant.

Here is my current code

It seems I cannot use numpy.min to enforce an elementwise min between two vectors. Additionally, I tried the basic min() but this wouldn't have the desired elementwise behavior and gives an error message prompting me to use .any() or .all().

I am requesting help to solve this system with FiPy.

thank you

[guyer]

I'm not seeing a way to do this with FiPy. An equation in FiPy is really an operator on the solution vector. Ultimately, what FiPy is doing is applying a cell-centered finite volume discretization to a PDE, to build a matrix and right-hand-side vector, in order to solve for a linear algebra equation for the solution vector. I have no idea, even conceptually, how to represent the minimum of two different equations as a matrix stencil.

[lmanda7]

I was also trying the substitution $\min\{a,b\} = (a+b-|b-a|)/2$ since the software is able to handle abs().

If I remove the underlined abs() I get the solution $h=c$ as expected (good). Is there any way to apply the abs() with the ImplicitSourceTerm inside? (My earlier usage of the ImplicitSourceTerm was incorrect)

Thank you

[guyer]

I'm afraid I still don't see a way to do this with FiPy