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Re: Laplace-Operator with Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39017] Re: Laplace-Operator with Mathematica
  • From: "Axel Ligon" <LigonAP at web.de>
  • Date: Fri, 24 Jan 2003 05:07:50 -0500 (EST)
  • Organization: University of Wuppertal
  • References: <b0opti$biv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hendrik van Hees ( http://theory.gsi.de/~vanhees/ ) gave me the solution for
this problem:

For example:   2Dim  - Polar coordinates
------------
x = r Sin[a]

y = r Cos[b]

xvec = {x,y}

q = {r,a}

jacobian = Table[D[xvec[[mu]],q[[nu]]],{mu,1,2},{nu,1,2}]

gcov = FullSimplify[Transpose[jacobian].jacobian]

gcontra = Inverse[gcov]

g = Det[gcov]

grad = Table[D[phi[q[[1]],q[[2]]],q[[k]]],{k,1,2}];

Lapl = FullSimplify[1/Sqrt[g] Sum[D [Sqrt[g]
(gcontra.grad)[[j]],q[[j]]],{j,1,2}]]
-----------

It is going on for each coordinate systems in each dimensions.

many thanks to Hendrik

Axel


"Axel Ligon" <LigonAP at web.de> schrieb im Newsbeitrag
news:b0opti$biv$1 at smc.vnet.net...
> Dear newsgroup
>
> It is possible to calculate an Laplace-Operator with Mathematica???
> For each coordinate systems in each dimensions??
> If yes, how?
>
> Axel
>
> Ps.: I mean as Laplace-Operator "Nabla^2" not the
> Laplace-Beltrami-operator (it is a extention of the Laplace-Operator)
>
>
>




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