Working with Dyadics in mathematica

[Jason Sidabras]

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

[dh]

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