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>

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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?

>

>

> Jason

>

```

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