Re: Numerical integration over an arbitrary 2D domain
- To: mathgroup at smc.vnet.net
- Subject: [mg127151] Re: Numerical integration over an arbitrary 2D domain
- From: alfonso.pagani at gmail.com
- Date: Mon, 2 Jul 2012 22:17:02 -0400 (EDT)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jsrplf$d3r$1@smc.vnet.net>
Il giorno luned=EC 2 luglio 2012 11:29:19 UTC+2, Alexei Boulbitch ha scritt= o: > Hi all, > I am a new user of Wolfram Mathematica. I need to integrate > (numerically of course) generic functions above complex 2D domains. > For example, i would like to find the moments of inertia of an airfoil > cross-section. Is it possible? > My idea was to import a triangular mesh (list of nodes and element > connectivity) of the integration domain. Then integrate my functions > using a trapezoidal integration. How could i do this? > Thank you very much, > > Alfonso > > > Hi, Alfonso, > > Mathematica can solve multiple integrals, and there are function NIntegra= te= > [ ] doing them numerically with a possibility to use various numeric met= ho= > ds and precisions. Check Menu/Help/NIntegrate. > > You can, of course, also do a custom program, but I recommend to first tr= y = > this function. If you already have done so and faced difficulties, post d= et= > ails of your integrand and domain. Otherwise your question is too general= t= > o help you. > > Have fun, Alexei > > > Alexei BOULBITCH, Dr., habil. > IEE S.A. > ZAE Weiergewan, > 11, rue Edmond Reuter, > L-5326 Contern, LUXEMBOURG > > Office phone : +352-2454-2566 > Office fax: +352-2454-3566 > mobile phone: +49 151 52 40 66 44 > > e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu> Hi Alexei, thanks for your prompt answer. Before posting my question I already checked NIntegrate. Moreover I read "ADVANCED NUMERICAL INTEGRATION IN MATHEMATICA" from Wolfram Mathematica Tutorial Collection. However I have not found yet the solution to my problem. My integrands are the product of very simple functions of x and y. Subscript[F[x_,y_],s]:=x^l y^m; Where l and m depend on s. For the sake of simplicity, let F_1 and F_2 be as follows: Subscript[F[x_,y_],1]:=x; Subscript[F[x_,y_],2]:=y^2; For example, if I had a rectangular integration domain I would write as follows: Subscript[E,1,2] = Integrate[(Subscript[F, 1][x, y] Subscript[F, 2][x, y]), {x, -b/2, b/2}, {y, -h/2, h/2}] The problem is that I need to integrate F_1 * F_2 over an arbitrary complex domain (such as a potato section!). As a further complication, my domain could also be not simply connected. Therefore I need necessarily to import my domain in Mathematica. That's why my idea was to import a numerical mesh of the domain, ei to define my domain as composed by elementary (triangular) elements. I hope I was sufficiently clear. Thank you for your help, Alfonso