How to handle Nonlinear PDE with Division and Exponent?

4

Hi @jarvin,

A few helpful (hopefully) points to consider: first, it’s recommended to post minimal working code examples: Read before posting: How do I get my question answered?. Running this code

gives

  File "/home/connor/Documents/fenics/code.py", line 14
    clsdform_T = alpha * dolfin.inner(S * **expterm**, v)*dolfin.dx
                                          ^
SyntaxError: invalid syntax

It’s easiest for people to assist if they don’t have to debug your code. :slight_smile: It’s also recommended to post the full error message that you receive.

Second, don’t confuse the functions T and S with the function spaces on which they live. In your code, you have defined S and T as dolfin.FunctionSpaces. I’m not an expert, but I wouldn’t expect UFL operations to be supported on function spaces. Instead, you should use the test and trial functions in your weak form.

Exponentiation (using the UFL operator dolfin.exp) and division seem to work for me when I replace the FunctionSpaces S and T with the trial and test functions v, w, phi, and theta defined on those function spaces:

import dolfin

alpha = 1
beta = 1
gamma_s = 1

# Create the Mesh
mesh = dolfin.IntervalMesh(10, 0, 1)
T = dolfin.FunctionSpace(mesh, 'CG', 2)
S = dolfin.FunctionSpace(mesh, 'CG', 2)

# FEM Discretization
v = dolfin.TestFunction(T)
phi = dolfin.TrialFunction(T)

w = dolfin.TestFunction(S)
theta = dolfin.TrialFunction(S)

clsdform_T = alpha * dolfin.inner(theta*dolfin.exp(-beta/phi), v)*dolfin.dx
clsdform_S = -gamma_s * dolfin.inner(phi*dolfin.exp(-beta/theta), w)*dolfin.dx

(Please note that I have not attempted to determine the correct weak form for this problem.)

A final note: since you are solving a nonlinear problem, you should use Functions (not TrialFunctions) in your weak form, as the nonlinear Poisson demo explains.

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