# Where can I find coded examples of stochastic collocation applied to an elliptical PDE using smolyak sampling?

I'm having some troubles implementing a collocation method to solve a stochastic partial differential equation of the form:

$\nabla (a(x,w)\nabla u(x,w))=f(x,w)$ in $D$,
$u=g$ in $\partial D$
where $w$ is a vector of uniformly distributed random variables and a(x,w) is a randomly distributed coefficient.

I have read a few papers on the subject, and I have a very basic understanding of the theory behind using smolyak sampling in the collocation method. I think I could make a lot more sense of it by seeing how a particular example is coded from start to finish. I found this reference with code provided here for the galerkin method. I can't seem to find another example with the collocation method implemented.

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## 1 Answer

check this : http://people.sc.fsu.edu/~jburkardt/m_src/sandia_sparse/sandia_sparse.html this may help you. this is for just points. also this is very nice tool box http://www.ians.uni-stuttgart.de/spinterp/ you can generate the points in space and then use deterministic finite element solver to evaluate those points and then calculate the statistic of the responses.

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