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Re: FDTD method to solve Maxwell equations

• To: mathgroup at smc.vnet.net
• Subject: [mg128544] Re: FDTD method to solve Maxwell equations
• From: Roland Franzius <roland.franzius at uos.de>
• Date: Fri, 2 Nov 2012 00:44:26 -0400 (EDT)
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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/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