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ocastilloreyes / petgem

petgem is a parallel and high-order code for active-source (e.g. CSEM) and passive-source (e.g. MT) geophysics electromagnetic modeling in 3D arbitrary marine/land problems under anisotropic conductivities.
https://petgem.bsc.es
BSD 3-Clause "New" or "Revised" License
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How abou the Basic Function Form of 2-Dimensional Edge Element？ #1

Closed HaoWangCyy closed 5 years ago

HaoWangCyy commented 5 years ago

Hello, I'm very lucky to see your code of the 3D marine controlled-source electromagnetic (3D CSEM) method. I want to disturb you here，can you give the concrete expression of 2-dimensional basis function, such as 2-order edge element and 3-order edge element? I hope to get your reply.

ocastilloreyes commented 5 years ago

Hello,

Thank you very much for your interest in PETGEM.

Currently, 2D high-order basis are not implemented within PETGEM, mainly because we are more interested in the 3D case (in addition to the lack of time).

However, in case the linear elements, also referred to as "whitney elements", are sufficient to solve your problem, we have a Matlab implementation of the linear bases of Jianming Jin's book: Jin, JM (2015). The finite element method in electromagnetics John Wiley & Sons. The main disadvantage of these elements could be the accuracy and convergence rate, although this will depend on your problem.

If that were not the case, you can find the complete expression for high-order 2D bases in the following paper: Fuentes, F., Keith, B., Demkowicz, L., & Nagaraj, S. (2015). Orientation embedded high order shape functions for the exact sequence elements of all shapes. Computers & Mathematics with applications, 70 (4), 353-458.

I hope this is useful for you.

HaoWangCyy commented 5 years ago

Thank you very much for your reply and help！

ocastilloreyes commented 5 years ago

You are welcome!