On Dec 7, 2007, at 4:26 AM, Ondrej Certik wrote:
> > Hi, > > On Dec 7, 2007 6:50 AM, Joshua Kantor <[EMAIL PROTECTED]> wrote: >> >> I would be interested in helping with a PDE toolbox. I didn't want to >> work on it alone as I'm pretty sure I'd make some stupid design >> choices. It would be nice to start some work on PDE functionality in >> SAGE. > > I would be very interested in this. Especially with finite elements > solver. SciPy has some solvers, but even producing the element > matrices would > be enough. > For variational problems, I've already written code in Maple to derive the element matrices. I presented a paper on in at the Maple 2005 Conference. Unfortunately, I've been having a difficult time translating some of the things I did from Maple to Sage. It was only for 1D problems (since that was all I needed), but it is modular enough to extend to others. The code derives the mass and stiffness matrices and then outputs them as MATLAB functions. I wrote the code because I needed something that can handle rotating flexible beams. > > > Basically, the way the equation is defined just need SAGE.calculus. > But I would very much like this to be modular, so that we can use both > maxima and sympy as a backend, so that I can use this in my own > programs, because depending on the whole SAGE would be too much. > > However, it's a huge task. There are many related projects, mainly: > > http://www.fenics.org/wiki/FEniCS_Project > http://www.fenics.org/wiki/SyFi I know about both of these, but I had never heard of the symfe work. Interesting, since my Maple toolbox is called SFEM. There is also a package for Maple called femLego: http://www.mech.kth.se/~gustava/femLego/ It's design is about solving the PDE once it has been derived. It uses Maple to write Fortran code, and compiles it with its own code. I nearly ended up using this, but see below. > But let's discuss at least the design. Let's use the same design as > in: > > http://www.mathworks.com/products/pde/ There are some problems with its design. It is basically an early version of FEMLAB, and it puts its focus strictly on solving PDEs once the formulation of the PDE has already been done. If a Ritz approach is used, the formulation of the PDE is never explicitly done and this design can't handle it. Plus, for systems with multiple coupled variables, the Galerkin approach becomes very complicated. I know because my SFEM package was originally an attempt to derive the weak form for use in FEMLAB. > > or is there a better product out there? > > Ondrej The difficulty is that most products seem to be trying to replace the major FE packages, but even those who do symbolic work, don't put any focus on the derivation. If one is going to use the weak formulation, this can be difficult. Tim. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
