Regrading my interests, kind of everything, but I think this is not a practical approach, at least now, to start with. So, let me give an idea about my skills and then you decide how to use the best of them.
performing
analysis on highly complicated models that would include vector
functions in three dimensional space, and the presence of nonlinear
terms in such models will impose the need to adopt a fixed point scheme.
Add to that the need to high accuracy while maintaining a suitable
processing time and memory usage. Honestly, I do not think that Matlab
could be a suitable choice in that stage.
I
tried to search for a suitable software that can serve my purpose, but
it is either proprietary with no way to know what they offer, or open
source with limited capability and a whole new language to learn. May be
the best thing I have seen until now is OpenFOAM in the sense that it
can provide a way to describe your model the way you write it
mathematically. However, Octave is best in the sense that all you need
is to know M-language.
I
have seen your list of proposed projects, and the idea of building a
generalized library for finite element method is vital. You can hardly
find the needed components in one place, and most importantly in a
consistent manner. For example, there is this package "iso2mesh" which I
found lately and it can provide an amazing 3D mesh from a scanned
image. Yet, what if I do not have an image? What if I need to draw a
certain complex geometry?? In addition, how can I use the output? In
Matlab, as far as I know, you can only view functions in 3D using
multiple slicing or using isosurface and patch commands. This will not
help you even simulate a given function on that mesh.
As
a user, I would like to suggest a final goal: 1) Allow one to insert a
model in Tex format, 2) Allow one to draw the domain or insert the
geometry as a volumetric image, 3) Allow one to choose (or choose for
him based on the given problem) the iterative scheme to be used for
solving and the fixed point scheme to be used if needed. If we are
speaking about a generalized library then I should also be able to view
scalar solutions in 3D space and also a way to view vector functions in
3D space as well. Providing polynomials of arbitrary order is a must. In
my algorithm of tracking the interface I needed polynomials of order no
less than 3; how can we optimize the performance in such situations. I was happy when I saw most of these ideas already on your list of future projects.
Well, I do not want to be long, I was just trying to give an idea about what I have in mind. I am right now reading the resources you provided to get a better insight, and it would also be great to meet the colleagues interested into that same line of development.
We will be in touch. Have a nice day,