# 9 point laplacian

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 November 25, 2011, 20:10 9 point laplacian #1 Member   valerio Join Date: Jun 2009 Location: Nancy Posts: 30 Rep Power: 10 Goodmorning, I'm trying to solve a PDE (ex: dT/dt=Lapl(T)) and I would try to access the 8 points close to a cell "i" in order to calculate a 9 point laplacian. The idea it's to solve it in a esplicit way using a forAll loop on the internal mesh points of the domain. The mesh is regular and the domain is a square (nothing complicated). Can you please tell me, once that I start the farAll loop how to find the neighboors of (exemple) alpha[i]? and how they are ordered (N,S,E,W,NE,NW,SW and SE)? thank you Last edited by Alucard; November 26, 2011 at 03:59.

 November 26, 2011, 02:48 #2 Senior Member   Niels Gjoel Jacobsen Join Date: Mar 2009 Location: Deltares, Delft, The Netherlands Posts: 1,759 Rep Power: 29 Hello and good morning to you 1. You can get all of the neighbours including the cell, cellI, itself by using the following: Code: ```const labelListList & cellPoints( mesh.cellPoints() ); const labelListList & pointCells( mesh.pointCells() ); label count(0); const labelList & cps( cellPoints[cellI] ); forAll(cps, pointi) count += pointCells[cps[pointi]].size(); labelList allCellCells(count); count = 0; forAll(cps, pointi) { const labelList & pcs( pointCells[cellPoints[cellI]] ); forAll( pcs, celli) allCellCells[count++] = pcs[celli]; } // Do a sort and a unique to remove duplicates``` 2. You cannot be ensured any particular ordering at all, as the underlying mesh structure in OF is unstructured. Good luck, Niels

 November 28, 2011, 06:17 #3 Member   valerio Join Date: Jun 2009 Location: Nancy Posts: 30 Rep Power: 10 Thank you very much i try it (infact i solve a more complicated equation than the heat transfer one but I needed the 9 points stencil so your answer is really what I need) -- Best regards, Valerio

 November 28, 2011, 06:28 #4 Senior Member   Niels Gjoel Jacobsen Join Date: Mar 2009 Location: Deltares, Delft, The Netherlands Posts: 1,759 Rep Power: 29 Hi Valerio Good. BTW: Note that the outlined code also works in 3D, which would give you the entire 27 cell stencil. I typically use the std::sort and std::unique to truncate the list of cell labels. Best regards, Niels

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