Re: Working with Dyadics in mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg85407] Re: Working with Dyadics in mathematica
- From: dh <dh at metrohm.ch>
- Date: Sat, 9 Feb 2008 04:18:29 -0500 (EST)
- References: <fogih0$3jd$1@smc.vnet.net>
Hi Jason,
As far as I know, dyades are nothing else than special second rank
tensor in a special notation. Mathematica is geared towards tensor
notation. Therefore why not use tensor notation? Here is an example with
base vectors ei:
a= a1 e1 + a2 e2
b= b1 e1 + b2 e2
a b= a1 b1 e1 e1+ a1 b2 e1 e2 + a2 b1 e2 e1 + a2 ba e2 e2
the same in tensor notation:
a={a1,a2}
b={b1,b2}
a b would then correspond to a matrix:
Outer[Times,{a1,a2},{b1,b2}]={{a1 b1,a1 b2},{a2 b1,a2 b2}}
hope this helps, Daniel
Jason Sidabras wrote:
> Hello all,
>
> I am currently doing a project where I am working on dyadic green's
> functions for an electromagnetic problem.
>
> My question comes in on how to handle the dyadic in mathematica with
> the dot product of the source.
>
> Currently I create the dyadic using my N(x,y,z) and M(x',y',z') as:
> [...]
> KroneckerProduct[Nemn[m, n, x, y, z, kg[m, n]],Memn[m, n, xp, yp, zp, -
> kg[m, n]]]
> [...]
>
> This creates the correct dyadic for my problem. My issue comes in on
> how to handle the source integral:
>
> Integrate[
> Gp[x,y, z, xp, 0, zp] .MoA[xp], {xp, a/2, a}, {zp, -d/2, d/2}] +
> Integrate[
> Gp[x, y, z, a, yp, zp].MoB[yp], {yp, 0, b}, {zp, -d/2, d/2}] +
> Integrate[
> Gp[x, y, z, xp, b, zp].MoC[xp], {xp, a, a/2}, {zp, -d/2, d/2}]
>
> Am I missing something fundamental on how to handle the source
> integral? Is Dot[] the correct function to use here?
>
> Thank you in advance,
>
> Jason
>