Helhmholtz theorem, how to implement it in Matlab?

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Francisco 2012-9-3

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https://ww2.mathworks.cn/matlabcentral/answers/47261-helhmholtz-theorem-how-to-implement-it-in-matlab

Hi, I am working on modeling a system, and one of the initial conditions for this system is given in terms of the divergence of a vector field, and so looking at Helmholtz theorem I can in principle calculate the vector field, as the curl I am pretty confident can be made 0 as it is a constant of motion, but now when I want to implement the theorem I ran into some problems. The vector I am looking for can be written as

where phi equals

Now I have to calculate the integral in matlab for phi, where I know what div(V) is, but when in comes to implementing it in matlab I get stuck,as in particular I am looking at the 2D case, and div(V) will be a matrix, and can't seem to figure out how to perform 2D integration in matlab. Any help will be appreciated.