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) > > >