Vector Integration Proposal for GSoC feedback

[Faisal Riyaz]

Dear Developers,

Please provide your feedback on my GSoC proposal for Vector Integration.

Here is the link to the wiki.

https://github.com/sympy/sympy/wiki/GSoC-2020-Application-Faisal-Riyaz:-Implementation-of-Vector-Integration

It is still not complete. I am looking forward to your feedback.

Best regards

Faisal Riyaz

[Faisal Riyaz]

To view my GSoC proposal in google docs, please use the following link

https://docs.google.com/document/d/1Y1VZvpfhj2Dz1T7s8z54YSVkc4L7f_iQRkPjGX42k3A/edit?usp=sharing

I am looking forward to your comments.

Best

Faisal Riyaz

 

[Aaron Meurer]

The Google Docs document seems to not be filled out all the way.

Aaron Meurer

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[Faisal Riyaz]

I am sorry. Pasted the wrong link. Here is the correct link.

https://docs.google.com/document/d/1hfacSxzCB7znpgTMFet5DA9ETG-_RO2VC6ci3Wsn-Ws/edit?usp=sharing

I still have to complete some sections.

Thanks

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[Faisal Riyaz]

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

[Aaron Meurer]

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

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[Faisal Riyaz]

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

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[Alan Bromborsky]

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. 

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[Faisal Riyaz]

Thank you for your suggestions, Alan. For the GSoC, I will try implementing all the functionality for 3D as the vector package now only supports 3D. I will define a class for the tetrahedron. 

Unfortunately, I am not very familiar with BEM equations but I am looking into them.

Thanks

Faisal Riyaz

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[Faisal Riyaz]

Hello all,

If possible, please provide your feedback on this approach.

Thanks

Faisal Riyaz