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Topic: FDTD method to solve Maxwell equations
Replies: 4   Last Post: Nov 7, 2012 12:57 AM

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Ralph Dratman

Posts: 62
Registered: 5/13/11
Re: FDTD method to solve Maxwell equations
Posted: Nov 2, 2012 11:57 PM
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This also interests me. Suppose the problem were limited to free space --
would that be feasible with Mathematica?


On Fri, Nov 2, 2012 at 12:44 AM, Roland Franzius <roland.franzius@uos.de>wrote:

> Am 01.11.2012 08:19, schrieb fc266@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/AdvancedNumericalDifferentialEquationSolvingInMathematica/
>
> 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)
> with six components obeying the constraints of exterior differential forms
>
> Dt[Wedge[F_ik Dt[xi], Dt[xk]] = 0
>
> 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.
>
> In the present situation the given Mathematica NDSolve-methods can not
> handle such monster problems, monsters with respect to memory and time.
>
> --
>
> Roland Franzius
>
>






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