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

1 Answer

FDM method is used for finite geometric electromagnetic computation.

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In this complete element is divided into form of meshes.

From Poisson’s equation

$∇^2 v=0$

Since it’s a 2-D figure

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

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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

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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).

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

Advantage of FDM:

  1. This method is highly accurate, since it uses fien mesh.
  2. It is the only widely used method in time domain for solving general problems.
  3. Simple to implement than MOM or FEM.

Disadvantage of FDM:

  1. Meshing is inflexible
  2. Uncertainty about precision of boundaries
  3. Frequency domain finite difference formulation are available but never become popular for general problems.
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