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IFFT involving 3 wave-numbers for PDE

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Brato CHAKRABARTI on 31 Dec 2015
I was solving PDE (Stokes equation to be specific) in Fourier space. The PDE was in 3 dimension and I had three wavenumbers namely, (k1,k2 and k3) for three directions. I am confused with using ifft to get the solution in real space. I am providing some expression of relevant quantities:
if true
% code
k = [k1 k2 k3]; % The wave number vector
knor = norm(k); % magnitude of the wave vector
A = 1 + (knor)^-4;
ka = [A*k1 A*k2 k3]; % Another vector to be used
f = [f1 f2 f3]; % A force vector where I know values of each component
X = - i*(f*ka')/(k*ka'); % A solution for a relevant quantity in Fourier space, i = sqrt(-1)
Y = f*(eye(3) - k'*ka/(k*ka')); % Another quantity in fourier space. Please note that Y is a vector and will have three components
I need to find both X and Y in physical space. Y will have three components in x,y and z direction. I am confused about how to use ifft or ifft3 to get the solution. I appreciate your help and patience. Thank you!!

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