On 09/05/2016 06:04 AM, hanks0...@gmail.com wrote:
K_Inv[0][0]=2*r/(cos(theta)*cos(theta)),
K_Inv[1][1]=2*r/(sin(theta)*sin(theta)), K_Inv[2][2]=r
r is calculated by "r=sqrt(x^2+y^2) ", and theta is calculated by "theta=x/y"
But, as you can expect that ,on the points where |x|<0.0000001 or
|y|<0.000001, cos(theta) or sin(theta) is almost zero. So, It seems that It
causes the singularity.
So, At first I tried to change the above 2 element in K_Inv like this...
K_Inv[0][0]=2*r/(cos(theta)*cos(theta)+del)
K_Inv[1][1]=2*r/(sin(theta)*sin(theta)+del),
Instead of this approach, you should use the following: if r>delta, use the
formula above. If r<=delta, use l'Hopital's rule to get an expression that
avoids the division by zero.
That said, you still have a problem for those values of x,y where theta is
close to zero or one, but r is not. For example, for x=0, y=1, you have
r=1
theta=pi/2
cos(theta)=0
K_inv[0,0] = 2/0
You need to think about what you want to do with this situation.
Best
W.
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Wolfgang Bangerth email: bange...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/
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