I am facing difficulty in understanding the method properly I would really appreciate it if someone can explain it to me through an example. I really need to understand it first before I can implement it. Especially equation (3). Also, can I use parts of the poster in my proposal? @nsukumar I would really appreciate your help.
On Mar 30, 2017 3:56 AM, "Ondřej Čertík" <[email protected]> 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/8800fd2ab1553cd768ad743c44b3ed 00c111c368/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/CADDwiVDahaHDC3gahGr1xfzN%2B_kJ52g%2BM53bahy6BjPMLSCcxw% 40mail.gmail.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/CAK1F8%2BejxDXA4B%3Dvp3%2BzsVKKhvWpb1yncWK238-4nRp3i%2BJF8A%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
