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Explain in details FDM method also state advantage and drawback

Mumbai University > Electronics Engineering > Sem 5 > Electromagnetic Engineering

Marks: 10 Marks

Year: May 2015, May 2016

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FDM method is used for finite geometric electromagnetic computation.

In this complete element is divided into form of meshes.

From Poisson’s equation

$∇^2 v=0$

Since it’s a 2-D figure

$∇^2 v=\dfrac{d^2 v}{dx^2} ×\dfrac{d^2 v}{dy^2} \\ \dfrac{d^2 v}{dx^2}=\dfrac{v(i+1)- 2v(i)+ v (i-1)}{∆i^2}……..(1) \\ \dfrac{d^2 v}{dy^2}=\dfrac{v(j+1)- 2v (j)+ v(j-1)}{∆j^2}………..(2) \\ ∆i= ∆j=1 \\ \dfrac{d^(2 ) v}{dx^2} + \dfrac{d^2 v}{dy^2}=v(i+1,j)+ v(i,j+1)+ v(i-1 ,j)+ v(i,j-1)- ∆v(i,j)$

From the above diagram,

$4v_0=v_1+ v_2+ v_3+ v_4 \\ v_0=\dfrac{1}{4} [v_1+ v_2+ v_3+ v_4 ]$

For example –

Find out voltage on following object

For voltage $v_1$

$v_1=\dfrac{100+100+0+v_2}{4} \\ 4v_1- v_2=200…………(a)$

For voltage $v_2$,

$v_2={100+v_1+ v_3+ 100}{4} \\ -v_1+ 4v_2- v_3=200……(b)$

For voltage $v_3$,

$v_3=\dfrac{v_2+ 0+0+100}{4} \\ -v_2+ 4v_3=100…………(c)$

Solving equation (a)(b) & (c).

$v_1=69.64v \\ v_2=78.57v \\ v_3=44.64v$