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Numerical Integration, FEM application

Posted 10 years ago
Hi everyone,
I am trying to calculate a 2d Integral which has another 2d integral in the integrands. here is the setup:
 alpha = 1; sigma1 = 4; sigma2 = 1; phi = 0.5;
 a = 0.5*(Cos[phi]/sigma1)^2 + 0.5*(Sin[phi]/sigma2)^2
 b = 0.25*Sin[2*phi]*(-1*sigma1^-2 + sigma2^-2)
 c = 0.5*(Sin[phi]/sigma1)^2 + 0.5*(Cos[phi]/sigma2)^2
 A = alpha/(2*pi*sigma1*sigma2)
 
 t[x1_, y1_, x_, y_] := A*Exp[-1*(a*(x - x1)^2 + b*(x - x1)*(y - y1) + c*(y - y1)^2)]
 
 B2[x1_, y1_, x_, y_] := HeavisideLambda[x - x1, y - y1]

trans:= NIntegrate[B2[x1, y1, xz, yz]*NIntegrate[t[xz, yz, xp, yp]*(B2[x2, y2, xz, yz] - B2[x2, y2, xp, yp]), {xp, x2 - 10*sigma1, x2 + 10*sigma1}, {yp, y2 - 10*sigma2, y2 + 10*sigma2}], {xz, x1 - 1, x1 + 1}, {yz, y1 - 1, y1 + 1}]

trans[0,0,1,0]
trans[0,0,10,10]
trans[0,0,50,50]

I am trying to get numbers for trans[0,0,x,y]for different x,y, but I couldn't get any results yet. I tried analytic integration too (Integrate instead of NIntegrate) but it didn't help either.
I am quite new to Mathematica so I don't know what options in NIntegrate can help me here.
I have tried the same integral in Maple, there it works for some values of phi, and doesn't for others (so i'm sure the thing should some how work here too). for example, it works fine for phi=0, but for phi=0.5 it fails. For phi=Pi/4, it works but the results don't go to zero as x,y get far from zero (e.g. trans[0,0,50,50]), which is the expected behavior for this integral.
any ideas?
Thanks in advance
POSTED BY: Amir Delgoshaie
Posted 10 years ago
You probably want to change pi to Pi because Mathematica demands correct capitalization.

You also want to change

trans:= ...

to

trans[ variable1_, variable2_, variable3_, variable4_ ] := ...

and I cannot be certain what the names of those four variables should be from your code.
When you make this change then your definition of trans will match your use of trans[ 0, 0, 1, 0 ] etc.
Then we will be able to see if more changes will be needed.
POSTED BY: Bill Simpson
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