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I have already developed a working solution of the Finite Element Method to solve heat transfer problems using GPU and OpenCL using the Conjugate Gradient method. The main disadvantage of this method is high demand for memory. Moreover, in case of graphics cards memory is often very limited. I see two options:

  1. Create subdomains and swap parts of the mesh with host memory
  2. Use multifrontal methods

I have to take into account the specific architecture. Swapping could be very expensive. CG method is popular in the context of GPGPU computing but I cannot find any comparison between CG and multifrontal methods (in case of GPGPU). Can multifrontal method be faster then CG? This is a general question, in fact, it still depends on the implementation.

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Do you do global assembly of the matrices in the FEM code of yours? or do you use matrix-free implementations? (i.e. no explicit formation of the matrices) –  Allan P. Engsig-Karup Feb 20 '12 at 15:34
What preconditioner are you using and what is the domain like? A ten year old desktop using a good algorithm will beat a cluster of GPUs using a crappy algorithm. –  Jed Brown Feb 21 '12 at 2:09
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I don't know whether it helps you. Here, you'll find a link to libgeodecomp, a tool which employs customizable domain decomposition techniques (from the site). It can be used with GPUs as far as I know. If it helps you, vote me up ;-)

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It looks quite promising. Thank you. –  Krzysztof Bzowski Oct 9 '12 at 7:27
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