how to plot inverse of a vector field from one domain to another?

Question

Avishek Mukherjee 2021-8-9

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https://ww2.mathworks.cn/matlabcentral/answers/894912-how-to-plot-inverse-of-a-vector-field-from-one-domain-to-another

回答： KSSV 2021-8-9

Suppose I have two domains:

D1: A deformed annulus

D2: A perfect annulus with inner radius 0.71392 and outer radius 1.

I have a vector field in the perfect annulus that looks like the following:

Now I want to apply the inverse function to find the corresponding vector field in my deformed annulus. But the inverse function is given by a set of complex numbers as below:

1.9243 - 2.3448i

-1.8310 + 1.0974i

-0.9593 - 1.2293i

2.5280 - 0.0000i

0.3371 + 2.2727i

1.6976 + 1.9680i

-2.1892 - 0.4916i

0.0680 - 2.7720i

-0.7310 + 0.8907i

-1.7848 - 1.5396i

1.7735 - 0.5859i

2.1590 + 1.2940i

-1.6775 - 0.0824i

-0.1903 + 1.2832i

2.5517 - 1.3639i

-0.8730 - 2.4399i

-0.9501 + 1.6772i

0.5269 - 2.1037i

0.4784 + 1.5771i

How to use these set of complex numbers to create the vector field in the deformed annulus?

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KSSV 2021-8-9

What do you mean by deformed anulus exactly? How you got this? I suspect some concept is missing here. You need to explain your exact problem you trying to solve.

Avishek Mukherjee 2021-8-9

Sorry for the confusion.

A deformed annulus means an annulus but the inner and the outer boundaries are simple analytic closed curves instead of a circle.

I got the deformed annulus by creating a set of points on the inner boundary and defining a Fourier series with those points. Same for the outer radius. Here is what I mean by a deformed annulus:

Now I want the vector field from the perfect annulus to be mapped to the above deformed annulus. The vector field in the perfect annulus is shown below: