COSNOV_2D : Constructs the 2D (local mesh ---> global mesh) map
[nov]=cosnov_2d(npdx,nex,npdy,ney) computes the 2-index array nov:
nov(i,ie) = is the index, with respect to global ordering,
associated to node i of element ie.
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Input: npdx = number of nodes along x-direction inside
one element (the same in every element)
nex = number of elements along x-direction
npdy = number of nodes along y-direction inside
one element (the same in every element)
ney = number of elements along y-direction
Output: nov = 2-index array of local to global map,
size(nov)=[max(npdx*npdy),ne]
Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
"Spectral Methods. Fundamentals in Single Domains"
Springer Verlag, Berlin Heidelberg New York, 2006.0001 function [nov]=cosnov_2d(npdx,nex,npdy,ney); 0002 % COSNOV_2D : Constructs the 2D (local mesh ---> global mesh) map 0003 % 0004 % [nov]=cosnov_2d(npdx,nex,npdy,ney) computes the 2-index array nov: 0005 % nov(i,ie) = is the index, with respect to global ordering, 0006 % associated to node i of element ie. 0007 % 0008 % __________________________ 0009 % | | | | | 0010 % | 3 | 6 | 9 | 12 | Omega and spectral elements 0011 % | | | | | ordering 0012 % __________________________ 0013 % | | | | | 0014 % | 2 | 5 | 8 | 11 | 0015 % | | | | | 0016 % __________________________ 0017 % | | | | | 0018 % | 1 | 4 | 7 | 10 | 0019 % | | | | | 0020 % __________________________ 0021 % 0022 % 0023 % Input: npdx = number of nodes along x-direction inside 0024 % one element (the same in every element) 0025 % nex = number of elements along x-direction 0026 % npdy = number of nodes along y-direction inside 0027 % one element (the same in every element) 0028 % ney = number of elements along y-direction 0029 % 0030 % Output: nov = 2-index array of local to global map, 0031 % size(nov)=[max(npdx*npdy),ne] 0032 % 0033 % 0034 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0035 % "Spectral Methods. Fundamentals in Single Domains" 0036 % Springer Verlag, Berlin Heidelberg New York, 2006. 0037 0038 % Written by Paola Gervasio 0039 % $Date: 2007/04/01$ 0040 0041 ldnov=npdx*npdy; 0042 ne=nex*ney; 0043 nov=zeros(ldnov,ne); 0044 0045 % element 1 0046 0047 nov(:,1)=(1:ldnov)'; 0048 0049 % elements first column 0050 0051 k=ldnov-npdx; 0052 for ie=2:ney 0053 nov(:,ie)=(k+1:k+ldnov)'; 0054 k=k+ldnov-npdx; 0055 end 0056 kmax=k+npdx; 0057 0058 % other columns 0059 0060 nxm1=npdx-1; 0061 for iex=2:nex 0062 0063 % other rows, bottom elements 0064 0065 ie=(iex-1)*ney+1; 0066 for j=1:npdy 0067 k=(j-1)*npdx; 0068 nov(k+1,ie)=nov(j*npdx,ie-ney); 0069 nov(k+2:k+npdx,ie)=(kmax+1:kmax+nxm1)'; 0070 kmax=kmax+nxm1; 0071 end 0072 0073 % other elements 0074 0075 for iey=2:ney 0076 ie=(iex-1)*ney+iey; 0077 0078 % first row 0079 nov(1:npdx,ie)=nov(ldnov-npdx+1:ldnov,ie-1); 0080 for j=2:npdy 0081 k=(j-1)*npdx; 0082 nov(k+1,ie)=nov(j*npdx,ie-ney); 0083 nov(k+2:k+npdx,ie)=(kmax+1:kmax+nxm1)'; 0084 kmax=kmax+nxm1; 0085 end 0086 0087 end 0088 end