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

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?

[KSSV]

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]

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:

Answer 1

[KSSV]

As you have the (x,y) for deformed annulus, you can go ahaead with the same procedure to get the vectors, isn't it?

If the given complex numbers are obtained from fft, have a look on ifft. Carry on inverse fft.