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I work in the field of Finite Element Methods, specifically, developing algorithms to speed up the computational time in structural mechanics problems. Till now I have been developing my code in Octave/Fortran and testing out my algorithms on small/simple problems (number of degrees of freedom less than 1000). Now I want to test out the algorithms on relatively large problems (number of degrees of freedom > 10000). To implement my algorithms, I need access to the system matrices: Mass, tangent Stiffness, Damping matrices, so that I can construct my reduced order model.

I would like to know which opensource FEA software (e.g., Calculix, Elmer, Tahoe or any other software) allows easy access and exchange of such information.

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    $\begingroup$ Thank you for your reply. I will look at the finite element libraries that you have mentioned and also look at Tim Davis's sparse matrix collection. On reading your side remark I did realize that I had made a typo (missed a 0) in my original posting. $\endgroup$ – Salil S. Kulkarni Mar 15 '17 at 12:48
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All of the major finite element libraries (such as libMesh; FEniCS; or the project I run, deal.II) provide you with ready access to the system matrix and or any other matrices you need. They typically also have tutorials and examples from a wide variety of areas (e.g., structures, fluids, etc) that you can use to generate examples.

Maybe a simpler first step, however, is to take a look at Tim Davis's collection of matrices: http://www.cise.ufl.edu/research/sparse/matrices/list_by_id.html . These contain examples from a number of areas and you can search the collection for specific examples.

I'm going to end on a side remark: "relatively large problems" would today have far more than the 10,000 degrees of freedom you quote in your post. I would say that everything under 100,000 is small today, and everything over 1,000,000 is large if you think of solving things on a single computer.

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    $\begingroup$ I would like to add to the previous answers that modern algorithm development must generally take into account the parallelism aspect. For instance, if you develop a method that is 2x as fast on a serial computer, but that leads to great communication cost and is slower when run in a distributed environment, it is much less interesting. Like Wolfgang mentioned, less than 100 000 DOF means relatively small problems that can generally be run on a desktop computers easily... $\endgroup$ – BlaB Mar 14 '17 at 13:54

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