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 >