RBF Interpolated Values Look Off

[Fuad-HH]

I was trying to fix the Interpolation Class Test that I am adding in #178 and found that the interpolated values look incorrect. The idea of the test is that I start by calculating sin(x) cos(y) + 1 for the node coordinates (top). Then I average the node values to the centroids (bottom middle). Then I tried to interpolate back from the centroids to the nodes using the RBF interpolation. I tried both the adjacency-based search method (bottom left) and my pointcloud-based (n-squared) search method (bottom right) to interpolate the centroid values to the nodes. The two pictures are for 10 by 10 and 20 by 20 element cases, respectively.

I did not make them use the same scale to show that the "trend/shape" of the field remains the same, but the values are lower everywhere. My initial concern is, even though the field can get averaged out, how can it get lower than 1 everywhere?

[Fuad-HH]

@abhiyanpaudel , @jacobmerson

[Fuad-HH]

@abhiyanpaudel helped me identify the problem. I was about the interpolation parameter lambda and decay_factor. I had to make them 0 and 5 from 10 and 15, respectively. If I remember correctly, I had to make them 10 and 15 for another case. I am making these variables available to the FORTRAN API. It would be great if there were documentation explaining what these are and when to use each one.

This issue is partially solved in d9bd71f. But the neighbors are still not matching. I will need to merge the two versions of radius adaptation.

[Fuad-HH]

This issue was solely due to lambda and decay_factor. Fixed it in #178.