I would suggest calculating for a geometric simplex
https://en.wikipedia.org/wiki/Simplex
since simplexes are the building blocks for finite element method
calculations. I think one of the main applications of your package
could be for calculating the boundary element method equations for
various problems.
On 3/30/20 12:54 AM, Faisal Riyaz wrote:
I am looking at the Maple functionalities for vector Integration. I
think Maple has the best functionality for vector integration among
other CAS.
https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student%2FVectorCalculus%2FSurfaceInt
https://www.maplesoft.com/support/help/Maple/view.aspx?path=Student%2fVectorCalculus%2fint
They have many different classes for commonly used surfaces and
curves. Some of them are
Circle
Ellipse
Sphere
Sector
Box
Triangle
For integration over Surface, I suppose I have to calculate the unit
normal vector. Parametrix representation of the surface needs to be
determined. And represent the differential area in terms of
parameters. This differential element will be associated with every
surface. Then represent the given vector/scalar field in terms of
parameters of the surface. Then the required integration can be easily
performed. Also, the direction of normal vector needs to be determined.
Similarly, for integration over curves, we have to calculate the
differential line element. Represent the line element and
scalar/vector field in terms of parameters.
Finding a parametric representation of well-known surfaces is easy but
it can be difficult for some surfaces.
I am going in the right direction. Please suggest. Also, who will be
the potential mentor for this project?
Thanks
Faisal
On Mon, Mar 30, 2020 at 7:33 AM Aaron Meurer <[email protected]
<mailto:[email protected]>> wrote:
Discussing the implementation would be more important. You don't need
to have actual code (other than possibly pseudocode). The API you
suggested would probably end up being something different, but the
implementation would be the same regardless of the API.
Aaron Meurer
On Sun, Mar 29, 2020 at 7:23 PM Faisal Riyaz
<[email protected] <mailto:[email protected]>> wrote:
>
> Hello All,
>
> Any suggestions? I will add functions for relating line integral
and surface integral (Stoke's Theorem and Green's Theorem). I do
not still know how difficult will it be. Also, In my proposal, I
have tried to provide the API of the functions. Is it enough or
should I also give a rough implementation? Feel free to comment
here or the google docs.
>
> Thanks
> Faisal Riyaz
>
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