Hi,
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I need to map data (scalar, vector, tensor) from a FDM grid to a FEM mesh. The girds or mesh are different from each other and the grid do not necessarily be equal spacing like the image below. Also, it can also be FEM to FEM mapping with different mesh.
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What I did is, made up my own method that maps nodal data from FDM to nodal data to FEM.
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I like to know the existing methods to do this data mapping. A book or review paper would be highly appreciated.
I think that one issue is the quality of the mapping you are asking for. If you have a FD solution on the regular structured grid having a certain order of accuracy you would retain the same accuracy after the mapping on the unstructured one.
Thus, a node on the unstructured grid has a value mapped by the congruent interpolation on the structured one.
What about the accuracy order of the FD solution?
Thanks a lot Denys Dutykh
. Those concepts of "generating continuous model" would be very helpful.I am trying to develop or adopt a Fast mapping process, so along with the method, computational complexity is also my great interest.
Right now, the FDM mesh is structured, but later on, Unstructured grid can come in way, so that would be a problem.
Thanks Filippo Maria Denaro ! I will dig into "congruent interpolation method".
I don't understand about the accuracy order exactly. For the Scalar variable that has to be solved using FDM is likely 1st order, but has much higher node density than FEM.
For mapping the scalar from FDM to FEM, I have used Central difference approach, but the method can be completely new. I need to dig literature to understand more.
Adnan Shahriar
if you start from a discrete FD solution, first order accurate, you can map in a very simple way the values on the unstructured grid. Just take each node of the unstructured grid and get the values by interpolatin on a 4-node molecule using bi-linear interpolation. You need only to find the correct stencil for each node but is is straighforward.
Thanks Filippo Maria Denaro . I probably has already incorporated the Method, just did another TSE for assigning Node coordinates to Array indices. It would be great to discuss with you in email if possible.
Thanks Denys Dutykh
. This is really a big boost for me! I will dig through the literature.
Hi Mikhail Shashkov . You mean this right?
https://en.wikipedia.org/wiki/Portage_(software)
This interpolation can be done by coupling libraries like PreCice, which is used for multiphysics applications like FSI.
Hope it helps.
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