Hi Vedarth, Thanks for your interest.
I think the best is to start writing the proposal and ask questions as you have them and I'll be happy to answer. Ondrej On Thu, Mar 30, 2017 at 2:09 AM, Vedarth Sharma <[email protected]> wrote: > I am interested. Can you guide me? > > > On Thursday, 30 March 2017 03:56:11 UTC+5:30, Ondřej Čertík wrote: >> >> Hi, >> >> Here is another GSoC idea from my collaborator at UC Davis, prof. >> Sukumar [1]. His student Eric Chin gave me his permission to post the >> project here, see the attached project description and his poster with >> more details. >> >> The general idea is to implement a module in SymPy to help integrate >> homogeneous functions over arbitrary 2D and 3D polytopes (triangles, >> quads, polygons, hexahedra, and more complicated 3D elements). The >> applications are in extended finite elements which requires an >> efficient quadrature of a 3D function over the finite element (say a >> hexahedron). Other applications are computer graphics (ridid body >> simulations of solids) and to devise cubature rules on arbitrary >> polytopes. >> >> See the references in the attached document. They use the Stokes >> theorem and Euler theorem to transform the 3D integral (which >> otherwise would require a 3D quadrature --- very expensive) to >> integral over faces and eventually edges, and so it becomes much >> faster. Features needed from SymPy: >> >> * exact handling of integers and rationals >> * symbolic representation of homogeneous functions >> * symbolic derivatives >> * numerical evaluation >> >> At first it sounds technical, but this would be extremely useful even >> for my own work. The spirit is roughly in line of this module that I >> started and others finished: >> >> >> https://github.com/sympy/sympy/blob/8800fd2ab1553cd768ad743c44b3ed00c111c368/sympy/integrals/quadrature.py >> >> The ultimate application of this sympy.integrals.quadrature module are >> double precision floating point numbers in Fortran, C or C++ programs, >> however the reason it's in SymPy is that one can use SymPy to get >> guaranteed accuracy to arbitrary precision. In principle >> sympy.integrals.quadrature could also be implemented using libraries >> like Arb (https://github.com/fredrik-johansson/arb), but Arb didn't >> exist when I wrote quadrature.py, and the code of quadrature.py is >> very simple, using regular SymPy, so there is still value in having >> it. >> >> The module proposed by this project would require symbolic features >> from SymPy as well, such as the symbolic derivatives, as well as the >> ability for the user to input the expression to integrate >> symbolically. >> >> The above project could also lead to a publication if there is interest. >> >> If there are any interested students, please let me know. I can mentor >> as well as help with the proposal. >> >> Ondrej >> >> [1] http://dilbert.engr.ucdavis.edu/~suku/ > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/612d52c0-5351-4b39-9030-bc6b178ff782%40googlegroups.com. > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CADDwiVA0p5G30s5UrD-AknjpDJhoSjNFvC1zxbbMfdtdmd_Jiw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
