How to make a polar grid with variable number of angular points?

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Mohamed Abd El Raheem 2022-2-20

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评论： Matt J 2022-2-21

Greetings...

I am making a grid to discretize a circular disk area for an integration process:

we have the radial variable ρ and the angle ϕ.
Making it using "meshgrid" (even with nonuniform ticks) yields a unnecessary large density of ϕ at small ρ and a poor density of ϕ at large ρ. This affects the convergence of the integral, and capturing the variaion on the disk will require to take inefficient very large grids.

Requirements:

Making the grid on varying density basis. That is, as the value of ρ increases, the number of ϕ samples increase.
The grid should be integrable in MATLAB. I mean, can we use trapz or any built in numerical integration function? Or do it using "sum" in a straight foreward manner?

Thanks in advance for any help.

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Answer 1

Matt J 2022-2-20

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编辑：Matt J 2022-2-20

I would use integral2() which, for one thing, does not require you to provide a meshgrid of samples. However, remember that with 2D integrals in polar coordinates, you have to multiply the integrand by ρ.