How to find the potential that corresponds to some particular (x,y,z) coordinate ?

Please I attached is a trajectory file from molecular dynamics simulation and potential matrix obtained by solving 3D Poisson equation.

The 3rd to 5th column are atomic positions and the 6th column is the charge density

The goal is to obtain potential by solving 3D Poisson's equation using finite difference method .

, where V(x,y,z) is the potential and rho is the charge density.

To begin with,I tabulated the charge densities over a 3D grid with the script below;

A = importdata('traj128_new.gro Charge.txt');

%%
x = str2double( A.textdata(3:end,4) ); % x positions 
y = str2double( A.textdata(3:end,5) ); % y postions
z = str2double( A.textdata(3:end,6) ); % z positions 
c = str2double( A.textdata(3:end,7) ); % charge

xx = linspace(min(x1),max(x1),60);
yy = linspace(min(y1),max(y1),60);
zz = linspace(min(z1),max(z1),60)
[xq,yq,zq] = meshgrid(xx,yy,zz); %query points


F = scatteredInterpolant(x,y,z,c); %Interpolant
rho = F(xq,yq,zq); % 3D charge density over a grid

I then use the charge densities tabulated over the grid to solve for the 3D potential. Both the charge density and the resulting potential are multidimensional arrays. My interest is finding the potential at some coordinate.

For instance say I have x =2.5, y = 3.5 and z = 4.5. My interest is in finding V(x,y,z), that is the the potential that corresponds to some coordinates in the volume.

Answer 1

[darova]

YOu are doing alright. Just pass to scatteredInterpolant values without NaN

ix = ~isnan(x+y+z+c);
F = scatteredInterpolant(x(ix),y(ix),z(ix),c(ix)); %Interpolant

[Anthony Owusu-Mensah]

Thanks for the response but my interest in not finding the value of the charge density at some specific coordinates. My interest is finding the potential at some specified coordinates. I have attached the potential matrix ( Potential_40MVm_trial1_traj128_new.gro+Charge.txt_.mat) which is a mutidimensional array.

That is to say from V which is the potential, what is the potential at some x = a, y = b and z = c.

[darova]

I don't understand. You have some (x,y,z) and c data and want to find some c0 value at (x0,y0,z0). You are doing this already and i show you some mistakes in your code

[Anthony Owusu-Mensah]

I used the (x,y,z) and c data to compute some value rho. I used the computed rho to solve for V. So given some coordinates x,y,z, what value in V corresponds to that coordinates.

Note = rho was computed using query points xq, yq and zq which is different from (x,y,z).

[darova]

im lost, sorry i can't help