stiff_2d_se

 STIFF_2D_SE Assembles 2D global SEM matrix associated to (nabla(phi_j), nabla(phi_i))_N


    [A]=stiff_2d_se(npdx,nex,npdx,ney,nov,wx,dx,jacx,wy,dy,jacy); 
        produces the matrix
        A_{ij}=(nabla(phi_j), nabla(phi_i))_N
        of size
        (noe,noe) where noe=nov(npdx*npdy,ne) is the number of d.o.f.

 Input : npdx = polynomial degree in every element along x-direction
         nex = number of elements (equally spaced) along x-direction
         npdy = polynomial degree in every element along y-direction
         ney = number of elements (equally spaced) along y-direction
         nov = local -global map, previously generated by cosnov_2d
         wx = npdx LGL weigths in [-1,1],
            (produced by calling [x,wx]=xwlgl(npdx))
         dx =first derivative LGL matrix (by calling dx=derlgl(x,npdx))
         jacx = array (length(jacx)=ne); jacx(ie)= (x_V2_ie-x_V1_ie)/2
         wy = npdy LGL weigths in [-1,1],
            (produced by calling [y,wy]=xwlgl(npdy))
         dy =first derivative LGL matrix (by calling dy=derlgl(y,npdy))
         jacy = array (length(jacy)=ne); jacy(ie)= (y_V3_ie-y_V1_ie)/2

 Output: A = matrix (noe,noe)

 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 [A]=stiff_2d_se(npdx,nex,npdy,ney,nov,wx,dx,jacx,wy,dy,jacy);
0002 % STIFF_2D_SE Assembles 2D global SEM matrix associated to (nabla(phi_j), nabla(phi_i))_N
0003 %
0004 %
0005 %    [A]=stiff_2d_se(npdx,nex,npdx,ney,nov,wx,dx,jacx,wy,dy,jacy);
0006 %        produces the matrix
0007 %        A_{ij}=(nabla(phi_j), nabla(phi_i))_N
0008 %        of size
0009 %        (noe,noe) where noe=nov(npdx*npdy,ne) is the number of d.o.f.
0010 %
0011 % Input : npdx = polynomial degree in every element along x-direction
0012 %         nex = number of elements (equally spaced) along x-direction
0013 %         npdy = polynomial degree in every element along y-direction
0014 %         ney = number of elements (equally spaced) along y-direction
0015 %         nov = local -global map, previously generated by cosnov_2d
0016 %         wx = npdx LGL weigths in [-1,1],
0017 %            (produced by calling [x,wx]=xwlgl(npdx))
0018 %         dx =first derivative LGL matrix (by calling dx=derlgl(x,npdx))
0019 %         jacx = array (length(jacx)=ne); jacx(ie)= (x_V2_ie-x_V1_ie)/2
0020 %         wy = npdy LGL weigths in [-1,1],
0021 %            (produced by calling [y,wy]=xwlgl(npdy))
0022 %         dy =first derivative LGL matrix (by calling dy=derlgl(y,npdy))
0023 %         jacy = array (length(jacy)=ne); jacy(ie)= (y_V3_ie-y_V1_ie)/2
0024 %
0025 % Output: A = matrix (noe,noe)
0026 %
0027 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0028 %                    "Spectral Methods. Fundamentals in Single Domains"
0029 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0030 
0031 %   Written by Paola Gervasio
0032 %   $Date: 2007/04/01$
0033 
0034 [ldnov,ne]=size(nov);
0035 noe=nov(ldnov,ne);
0036 A=sparse(noe,noe);
0037 for ie=1:ne
0038 Al=stiff_2d_sp(wx,dx,jacx(ie),wy,dy,jacy(ie));
0039 A(nov(1:ldnov,ie),nov(1:ldnov,ie))=A(nov(1:ldnov,ie),nov(1:ldnov,ie))+Al;
0040 end
0041 
0042 return