Various improvements to PHT method #7
Description
I don't know if there is much interest in upgrading this package but i noticed there have been several semi-recent papers with updates and fixes for PHT splines that could potentially be implemented. It's unclear to me if any of these are already applied in this project.
It's been noticed the original PHT spline technique suffers from a decay problem, which was addressed in this 2015 paper, but sadly the fix also destroys the partition of unity.
https://www.sciencedirect.com/science/article/abs/pii/S1524070315000302
But a recent paper then provided another fix for the previous method, fixing both the decay issue while maintaining the partition of unity.
https://www.techscience.com/CMES/v138n1/54227
There has also been an improved quadrature method specifically for IGA published that finds the optimal minimum required quadrature points for a given spline using the "Gauss–Greville" technique borrowing the best from several previous known methods. I might be wrong but i think this may already be implemented for the 1D section?
https://www.sciencedirect.com/science/article/abs/pii/S0045782522000871
I am aware this package isn't overly popular but it still appears to be the most used implementation of the PHT method available and of interest to maintain i believe. I'm only fairly new to coding and don't have much experience with matlab but i will look into seeing it if can apply any of these fixes. As this is open source i'm not expecting/requesting anything in particular to be done, just pointing some potentially useful developments. Would be interested to know other's thoughts.