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'Variable Coefficient Matrix' Poisson Equation

Asked by Alex Evans

I am trying to solve the 2D Poisson equation: Div( k grad(p))=0 where k is a diagonal matrix.

I have tried the following attempt to modify existing code for a variable coefficient solver (after importing numpy and dolfin)

------------------
k=zeros(2,2)
k[0][0]=Expression("1")
k[1][1]=Expression("2")

a = inner(k*nabla_grad(u), nabla_grad(v))*dx
------------------

The error is generated once I have put these lines in as shown. (The solver works for a=inner(k*nabla_grad(u),nabla_grad(v)) as expected (where k is a scalar expression)).

The error given is that numpy arrays can't have expressions as arguments. How should I get around this? Or if there a very different way i should be approaching this problem?

Cheers

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Felix Ospald
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Best Felix Ospald (felix-ospald) said : 		#1

I think you have to write

k = as_matrix(((Expression("1"), 0), (0, Expression("1"))))

or have a look at the undocumented/tensor-weigthed-poisson demo

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Alex Evans (evansalex) said : 		#2

Thats great - its at least fixed that step...could you send me the url for that demo by any chance? Can't seem to locate it.

Cheers

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Felix Ospald (felix-ospald) said : 		#3

http://bazaar.launchpad.net/~dolfin-core/dolfin/trunk/view/head:/demo/undocumented/tensor-weighted-poisson/python/demo_tensor-weighted-poisson.py