For the 2D Poisson equation, there exist on finite difference mesh, some code taking $O(n \log(n))$ operations to solve it on a mesh with $n$ nodes. They rely on Fast Fourier Transform or Block Cyclic Reduction.

Is there anything as fast on unstructured meshes? I am afraid no, but fast solution of Poisson equation on unstructured meshes is a common problem. Any known efficient solution method?

  • $\begingroup$ Hi @MathieuDutourSikiric, and welcome to Scicomp! Have you looked at this method: math.nyu.edu/faculty/greengar/poiss2d.pdf $\endgroup$
    – Paul
    Nov 22 '12 at 15:01
  • 1
    $\begingroup$ Should not finite element discretization with a multigrid solver for the resulting system of linear equation do it in $O(n)$? $\endgroup$
    – Thomas W.
    Nov 23 '12 at 6:10

Multigrid solves the Poisson equation with complexity $O(n)$ which is the optimal possible complexity.


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