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How can I solve the equation of curvature on PDE Toolbox?

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Sarojeet Deb
Sarojeet Deb on 25 Oct 2017
The equation is ∇n̂=2*curvature, Curvature is a constant
n̂ = ∇f/∥∇f∥ (Unit normal)
Here f is f(x,y)
I made the geometry in PDE Toolbox, meshed it and inputted the values in PDE Toolbox. But I am unable to input ∥∇f∥. I want to be ||∇f||= sqrt(x^2+y^2+u^2)

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Answers (1)

Precise Simulation
Precise Simulation on 26 Oct 2017
Edited: Precise Simulation on 29 Oct 2017
∥∇f∥ should typically be sqrt(fx^2+fy^2+eps) where eps is a small constant to avoid divisions by zeros (since ∥∇f∥ is in the denominator). As this look like a Hamilton-Jacobi distance function problem another approach would be to transform the equation to a time dependent one, which should be somewhat easier to solve.

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Precise Simulation
Precise Simulation on 31 Oct 2017
Yes, if your function 'f' is labelled 'u' in the pde implementation.

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