Calculating the laplacian of a complex field

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Nick Keepfer 2020-8-31

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https://ww2.mathworks.cn/matlabcentral/answers/586928-calculating-the-laplacian-of-a-complex-field

编辑： Nick Keepfer 2020-8-31

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I'm trying to solve a Nonlinear-Schrodinger equation that contains a laplacian term

I know that you can use the

del2(psi,x,y)

command. But I wish to do this in Fourier space, and without using any inbuilt functions as I am porting the code over to fortran.

So far, I have the code

%% Setup of grid and Fourier grid/operators
xmax = 15;
xmin = -15;
ymax = 15;
ymin = -15;
nx = 1024;
ny = 1024;
dx = (xmax-xmin)/nx;
dy = (ymax-ymin)/nx;
x = [xmin+dx:dx:xmax];
y = [ymin+dy:dy:ymax];
kx = 2*pi/(xmax-xmin)*[0:nx/2 -nx/2+1:-1];
ky = 2*pi/(ymax-ymin)*[0:ny/2 -ny/2+1:-1];
Tx = - kx .* kx;
Ty = - ky .* ky;
%% Load wavefunction
load('psi.mat')
psi = psiR + 1i.*psiI;
%% Move to fourier space
kpsi = fftn(psi);
%% Calculate laplacian using both methods
delsqLaplacian = 4*del2(u_og,x,y); % using del2
fourierLaplacian = ifftn((Tx + Ty').*kpsi)*(4*pi*pi/((xmax-xmin)*(ymax-ymin))); % Using Fourier derivatives