Evaluate function and gradient along edge with pde toolbox

Dear Matlab community,

I do solve a heat diffusion equation in a 2D problem. My geometry is composed of a circular source region inserted into a bigger square domain. When the computation is done I wish to evaluate the value of my field (u(x,y,t)), as well as its gradient, along the edge between the two previous regions. I know that we can evaluate the gradient with specific coordinates, but I wish to evaluate it at the boundary of the circular region.

Is there a direct way to do it by simply specifying the label of the edge boundary? Or should I create a trajectory which matches as close as possible?

Best

Answer 1

[Alan Weiss]

Depending on your toolbox version, there are several ways of doing this. In R2016a and later, the evaluateGradient function enables you to evaluate (interpolate) the gradient at arbitrary points, including along the boundary. In earlier toolbox versions, you can use the pdegrad function to give the gradient in each mesh triangle (the gradient is constant in each triangle because the basis functions are linear).

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[nicolas bachelard]

Dear Alan,

I used evauateGradient along a querypoints trajectory that I defined myself already. Do you have any idea how I could specify to evaluateGradient to operate along a specific boundary?

Best