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Re: FDTD method to solve Maxwell equations

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  • Subject: [mg128571] Re: FDTD method to solve Maxwell equations
  • From: fc266 at st-andrews.ac.uk
  • Date: Sun, 4 Nov 2012 20:13:13 -0500 (EST)
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On Friday, November 2, 2012 5:13:46 AM UTC, Roland Franzius wrote:
> Am 01.11.2012 08:19, schrieb fc266 at st-andrews.ac.uk:
>
> > Hi All,
>
> >
>
> > I am new to Mathematica and I want to advance my knowledge of Electromagnetic wave propagation. Using the FDTD method I would like to solve Maxwell's equations and simulate different systems. I understand the physics but I have no idea how to translate that to Mathematica, so if anyone can help me to write and understand a code for this that would be great! Thanks a lot!
>
> >
>
>
>
>
>
> Perhaps you should first work with the NDSolve tutorial you can download
>
> here
>
>
>
> http://www.wolfram.com/learningcenter/tutorialcollection/AdvancedNumerica lDifferentialEquationSolvingInMathematica/
>
>
>
> NDSolve has an optional parameter "Method -> xy". The predefines method
>
> values reflect the current state of art in the translation of existing
>
> high speed-high accuracy methods from the supercomputer area to computer
>
> algebra systems.
>
>
>
> To implement a NDSolve method in 4 space time dimensions for the Maxwell
>
> second rank tensor field
>
> (t,x)-> F_ik(t,x)
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> with six components obeying the constraints of exterior differential forms
>
>
>
> Dt[Wedge[F_ik Dt[xi], Dt[xk]] = 0
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>
>
> is probably a very ambitious project and not so much a suitable working
>
> field to learn the application of Mathematica to real space-time physics.
>
>
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> In the present situation the given Mathematica NDSolve-methods can not
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> handle such monster problems,  monsters with respect to memory and time.
>
>
>
> --
>
>
>
> Roland Franzius

I would just be interested in solving for the 1D and 2D case so I can simulate some basic examples, how would I be able to do that? is that simpler?



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