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[Lapack] Poisson solver

Dear LAPACK team,

I would like to solve a (2D) Poisson equation on a uniform grid of about 256 by 
256 points with a Dirichlet boundary condition.

That is, I want to solve a linear system with a sparse matrix that has size of 
about (256*256) by (256*256).

Could you tell which Lapack routine would be optimal (fast and precise) in this 
respect? Or where I can find documentation on that? That would be great.

Thanks in advance and best regards,

Jan Viebahn
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