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Does anyone have any numbers on how mathematica compares to other commercial (eg ANSYS) or free FEM softwares (eg. FreeFEM++, FEniCS, elmer)? If this is too vague say solving the diffusion equation in a 2D region and how does it scale with the number of elements on the region.

My boss wants me to switch to a c-based fem solver and I'd like to have an idea of how much speed up I will get before migrating all my code.

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  • $\begingroup$ Did you do any benachmarking yourself after you switched the code? $\endgroup$
    – user21
    Commented Jun 10, 2016 at 1:00
  • $\begingroup$ Not yet. I went as far as reading the documentation of Free-FEM. Terrible. Plus it works with the integral formulation so I had to rewrite my code. Now we want to do it in 3D so may be worth it to try other packages, but it's not the main focus of the research. I'm using fem only to solve the interaction force between colloidal particles so once I get an approximation for the force between the particles as a function of the distance I switch to the ODE system with that force and study there the phase-space. Way faster. $\endgroup$
    – tsuresuregusa
    Commented Jun 10, 2016 at 1:21
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    $\begingroup$ While I am confident that the performance of the FEM code in Mathematica is not bad it does also come with good documentation (I hope); that's worth something too, is it not? $\endgroup$
    – user21
    Commented Jun 10, 2016 at 1:38
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    $\begingroup$ well, if I can use myself as an example, I never learnt it before since the whole approach to it seemed utterly engineer-like, full of particular cases. The implementation of mathematica seems to be very robust and intuitive (after a while, there is a learning curve) and the examples are quite universal and easily expandable. Even if it were 10 times slower being able to write everything in mma is a great plus for me. Besides the technical support is quite knowledgeable ;) $\endgroup$
    – tsuresuregusa
    Commented Jun 10, 2016 at 2:25

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