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/ >
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