Ok, I have a strong problem. It has to do with programming and concepts of mathematics.(adsbygoogle = window.adsbygoogle || []).push({});

I have a coordinate transformation:

[tex] x=x(\xi,\eta)[/tex]

[tex] y=y(\xi,\eta)[/tex];

and I want to calculate the metrics coefficients:

[tex] \xi_x=\frac{\partial \xi}{\partial x}[/tex]

[tex] \eta_x=\frac{\partial \eta}{\partial x}[/tex]

[tex] \xi_y=\frac{\partial \xi}{\partial y}[/tex]

[tex] \eta_y=\frac{\partial \eta}{\partial y}[/tex]

But I have only the next (I only have the numeric transformation, I don't have any analytical formulae):

x= a matrix of dimensions [tex] n_{\xi}, n_{\eta}[/tex];

y= a matrix of dimensions [tex] n_{\xi}, n_{\eta}[/tex];

[tex] \xi[/tex]= a vector of size [tex]n_{\xi}[/tex]

[tex] \eta[/tex]= a vector of size [tex]n_{\eta}[/tex]

Well, I want to compute the metrics coefficients using central diferences. Please, tell me what would you do in order to compute it. I'm goind to show you what i made in Matlab:

for i=2:nxi-1;

for j=2:neta-1;

XI_x(i)=(XI(i+1)-XI(i-1))/(x(i+1,j)-x(i-1,j));

ETA_x(j)=(ETA(j+1)-ETA(j-1))/(x(i,j+1)-x(i,j-1));

XI_y(i)=(XI(i+1)-XI(i-1))/(y(i+1,j)-y(i-1,j));

ETA_y(j)=(ETA(j+1)-ETA(j-1))/(y(i,j+1)-y(i,j-1));

end

end

I'm not sure it works, because I'm not able to imagine the metrics coefficients just acting upon the functions x and y. I don't know If i'm taking correctly the variations in x and y in the denominators.

Any advice will be greatly appreciated.

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# Coordinate Transformation

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