Numerical Integration of 2D Unstructured Data

Hi, I assume this is a question that has multiple answers, but I seem to not be searching correctly.

• i have a solution to a 2D problem on an unstructured grid (grid shown below)
• the results are stored in an (nx*ny,1) vector. i.e I have (x, y, f(x,y)) as a [nx*ny,3] vector
• I need to integrate over the domain. I am aware of the trapz approach for 2D cases, but in my experience so far, this only works if the grid is cartesian (i.e there are nx unique values of x and ny unique values of y).
• I tried some other suggestion to: fit the data to scatteredInterpolant, create an inline function, then use integral2, but this takes a lot of time and I need to repeat this for about 13000 data points. (about 15 seconds, so I will ne needing about 2 days for this)
• is there any way I can speed this up (I have tried reducing the absolute and relative error settings, to arrive at this new 15 seconds time)
• 

[Torsten]

I always sum over the area of the triangle multiplied by the (approximated) value of the function in its center of gravity (in your case maybe the arithmetic mean of the values in the corner points).

[Uche Agbogwu]

okay then, thank you I will give this a try.

Answer 1

[Uche Agbogwu]

My solution was to :

• check the interpolation approach; I realised from the surfaceinterpolant object, some data points were being extrapolated to unphysical values, so I changed this to "none" and added an extra line which removed the nan objects