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Is there an iterative sparse parallel solver with out of core capabilities? I need to solve a very large system of equations. I have implemented direct sparse parallel solvers in core and out of core and now I have to try an iterative one. Mainly I use FORTRAN for the implementation.

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    $\begingroup$ How big is "very large", and how sparse is "sparse"? Second, I presume you want to use an out-of-core solver because you do not have access to a cluster large enough to hold your matrix. Have you considered looking around for local, regional, or national resources that would give you more nodes and allow you to exploit the efficiency of one of the many libraries for sparse iterative methods? Finally, where does this problem come from? Will you have access to a decent preconditioner? $\endgroup$ – Bill Barth Apr 15 '15 at 17:24
  • $\begingroup$ Very large for me is over one million equations, sparsity is around 1%. My problem is not to just solve the system of equations, but to use many kinds of available solvers. My goal is to be able to solve such systems in any pc or workstation, so I am not interested in clusters. I have managed to do so using direct out-of-core solvers, but i can't find an iterative one. Is it so because iterative sparse solvers are not very memory demanding? My systems come from structural engineering. $\endgroup$ – kyperros Apr 16 '15 at 7:25
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For a sparse parallel solver, it's your own responsibility to provide a matrix vector product and a suitable preconditioner. The data for the vector itself should fit into main memory in any case. If the matrix has at most a fixed small number of non-zero elements (<20) per column or row, then the same is also true for the matrix itself. In this case, an incomplete LU preconditioner would not need out-of-core capabilities either, and otherwise it would be quite slow anyway.

In any case, I don't think that the iterative solver itself needs to take care of out of core capabilities, even for problems that need such capabilities.

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