I want to create a surface Laplacian under the spheroidal coordinates, Now, I already have the surface gradient defined, but I don't know how to find the Laplacian.
Since the surface gradient is too long, and it's a vector operator, I use this one as an example:
op[t_]:={Cos[t] D[#, t], Sin[t] D[#, t]}&;
Apply this on some u(t), I got:
In[540]:= op[t][u[t]]
Out[540]= {Cos[t] u'[t], Sin[t] u'[t]}
which is what I want.
However, I can't do divergence of this gradient. I've tried Composition, but it gives me a matrix instead of a scalar:
In[550]:= Composition[op[t], op[t]][u[t]]
Out[550]= {{Cos[t] (-Sin[t] u'[t] + Cos[t] u"[t]), Cos[t] (Cos[t] u'[t] + Sin[t] u"[t])},
{Sin[t] (-Sin[t] u'[t] + Cos[t] u"[t]), Sin[t] (Cos[t] u'[t] + Sin[t] u"[t])}}
which is obviously wrong.
So, how can I get the Laplacian? Please help!