Calculating Mesh curvature at the boundary for every point

mesh
1

Hey,
Is there any inbuilt method in FEniCS to compute the radius of curvature at the boundary points?
I have been using numpy gradient method to evaluate the first and second order derivatives of x and y coordinates and using the derivatives, calculate the value of curvature at each mesh boundary point.

K = |x’ y’’ - y’ x’’|/((x’)^2 + (y’)^2)^1.5

This is the equation I am using to find the curvature at every mesh boundary point.

Thank You

2

In FEmorph, there are several different options for computing mean curvature, see: FEmorph pip installable branch. line 265-365.

3

Could You kindly inform me which version of FEniCS is being used here? I am currently working on 2019.1

4

Hi,
I guess this is 2018.1.0. I haven’t had time or any reason to update this library.

5

Hello Dokken,

I had tried computing the value of curvature of a circular mesh using FEmorph, but the values of the curvature at the boundary while computed using kappa = ComputeDivNVolume(mesh, CurvSmooth) gives me values that are smaller than the actual values of the curvature at the boundary. I had used the same on a circular mesh with radius 10 and the curvature came out to be kappa(0,10) = 0.0983785276 whereas the actual curvature value should be 0.1 .

Is there anything that I might have done that might be causing this variation in curvature

6

Dear Akhil
Did you solve this problem? If so, could you kindly post a reply for the same. Alternately, could you kindly post the code snippet for your original method of computing curvature from the derivates of the boundary position vector?
Thanks

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