TF/SF Taflove Computer Implementation

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Chris Fadden

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I am trying to implement my own 3D FDTD based on Taflove's book, however I'm running into trouble with my TF/SF implementation. I am attempting to model free space, with no scatterers, yet I am getting significant fields outside the Total Field region. I am modelling a 10 GHz sine wave with a deltax of 0.002.

I don't expect you to debug my code, but if anyone has an implementation of the fully general 3D TF/SF, not just in one direction, that would be fantastic. I am confident that I have accounted for the 1/2 offsets correctly, but I would like to confirm.

Thanks for your help

Code: 
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[TD="colspan: 2"]Code C - [[COLOR=#226C22]expand[/COLOR]][/TD]
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[/TD]
[TD][COLOR=#993333]void[/COLOR] FDTD[COLOR=#339933]::[/COLOR][COLOR=#202020]TFSF[/COLOR][COLOR=#009900]([/COLOR][COLOR=#009900])[/COLOR]
[COLOR=#009900]{[/COLOR]
  [COLOR=#993333]int[/COLOR] i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#339933];[/COLOR] 
  
 
  [COLOR=#808080][I]/******************[/I][/COLOR]
[COLOR=#808080][I]   * Y Face H Updates[/I][/COLOR]
[COLOR=#808080][I]  ******************/[/I][/COLOR]
  
  [COLOR=#666666][I]//Initial Y [/I][/COLOR]
  j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933];[/COLOR]
   
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hz[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]ExInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hx[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
  [COLOR=#666666][I]//Final Y[/I][/COLOR]
  
  j [COLOR=#339933]=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hz[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]ExInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hx[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
 
  [COLOR=#808080][I]/********************[/I][/COLOR]
[COLOR=#808080][I]   * Z Face H Updates[/I][/COLOR]
[COLOR=#808080][I]   *******************/[/I][/COLOR]
  
  [COLOR=#666666][I]//Initial Z[/I][/COLOR]
  k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hy[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]ExInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hx[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#666666][I]//Final Z[/I][/COLOR]
  k [COLOR=#339933]=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hy[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]ExInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hx[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#808080][I]/*****************[/I][/COLOR]
[COLOR=#808080][I]   *  X Face H Updates[/I][/COLOR]
[COLOR=#808080][I]   ****************/[/I][/COLOR]
   
  [COLOR=#666666][I]//Initial X[/I][/COLOR]
  i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hz[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
   
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR] 
      Hy[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933]+[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
 
  [COLOR=#666666][I]//Final X[/I][/COLOR]
  i [COLOR=#339933]=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR]
 
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hz[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR]  Ce1D[COLOR=#339933]*[/COLOR]EyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Hy[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ce1D[COLOR=#339933]*[/COLOR]EzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  
  
  [COLOR=#808080][I]/****************** [/I][/COLOR]
[COLOR=#808080][I]   * Update 1D Grid [/I][/COLOR]
[COLOR=#808080][I]   *****************/[/I][/COLOR] 
  Update1D[COLOR=#009900]([/COLOR][COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR] [COLOR=#666666][I]//Increment time for the 1D grid [/I][/COLOR]
 
  [COLOR=#808080][I]/**************[/I][/COLOR]
[COLOR=#808080][I]   * Y Face E Updates[/I][/COLOR]
[COLOR=#808080][I]   *************/[/I][/COLOR]
 
  [COLOR=#666666][I]//Initial y[/I][/COLOR]
  j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ex[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR] 
 
  j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ez[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D [COLOR=#339933]*[/COLOR] HxInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#666666][I]//Final Y [/I][/COLOR]
  j [COLOR=#339933]=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ex[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR] 
 
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ez[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HxInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
 
  [COLOR=#808080][I]/********************[/I][/COLOR]
[COLOR=#808080][I]   *  Z Face E Updates[/I][/COLOR]
[COLOR=#808080][I]   *******************/[/I][/COLOR]
  
  [COLOR=#666666][I]//Initial Z  [/I][/COLOR]
  k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] 
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR] 
      Ex[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
   
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ey[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HxInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
  [COLOR=#666666][I]//Final Z[/I][/COLOR]
  k [COLOR=#339933]=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ex[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR] i [COLOR=#339933]<=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR] i[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ey[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HxInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
 
  [COLOR=#808080][I]/**************************[/I][/COLOR]
[COLOR=#808080][I]   *  X Face E Updates[/I][/COLOR]
[COLOR=#808080][I]   *************************/[/I][/COLOR]
  
  [COLOR=#666666][I]//Initial X[/I][/COLOR]
  i [COLOR=#339933]=[/COLOR] TFSF_x0[COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ey[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR] 
      Ez[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933]-[/COLOR][COLOR=#0000dd]1[/COLOR][COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
  
  [COLOR=#666666][I]//Final X[/I][/COLOR]
  i [COLOR=#339933]=[/COLOR] TFSF_x1[COLOR=#339933];[/COLOR]
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<=[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
      Ey[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]-=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HzInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
  [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]j [COLOR=#339933]=[/COLOR] TFSF_y0[COLOR=#339933];[/COLOR] j [COLOR=#339933]<=[/COLOR] TFSF_y1[COLOR=#339933];[/COLOR] j[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR]
    [COLOR=#b1b100]for[/COLOR][COLOR=#009900]([/COLOR]k [COLOR=#339933]=[/COLOR] TFSF_z0[COLOR=#339933];[/COLOR] k [COLOR=#339933]<[/COLOR] TFSF_z1[COLOR=#339933];[/COLOR] k[COLOR=#339933]++[/COLOR][COLOR=#009900])[/COLOR] 
      Ez[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR] [COLOR=#339933]+=[/COLOR] Ch1D[COLOR=#339933]*[/COLOR]HyInc[COLOR=#009900]([/COLOR]i[COLOR=#339933],[/COLOR]j[COLOR=#339933],[/COLOR]k[COLOR=#009900])[/COLOR][COLOR=#339933];[/COLOR]
 
  [COLOR=#b1b100]return[/COLOR][COLOR=#339933];[/COLOR]
[COLOR=#009900]}[/COLOR][/TD]
[/TR]
[/TABLE]
[/LEFT]
 

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