ad_1d_se

 AD_1D_SE Assembles 1D global SEM matrix associated to ad operator -nu u'' + beta u'

    [A]=ad_1d_se(npdx,ne,nov,nu,beta,wx,dx,jacx); produces the matrix

        A_{ij}=(nu phi_j', phi'_i)_N +beta( phi_j' ,phi_i)_N of size

        (noe,noe) where noe=nov(npdx,ne) is the number of d.o.f.

 Input : npdx = polynomial degree in every element
         ne = number of spectral elements
         nov = local -global map, previously generated by cosnov1d
         nu   = viscosity (constant>0)
         beta = coefficient of first order term (constant)
         wx = npdx LGL weigths in [-1,1],
            (produced by calling [x,w]=xwlgl(npdx))
            (npdx = number of nodes, =n+1, if n=polynomial degree)
         dx = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
         jacx =  jacobian of the map F:[-1,1]---->[xa_ie,b_ie]

 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]=ad_1d_se(npdx,ne,nov,nu,beta,wx,dx,jacx);
0002 % AD_1D_SE Assembles 1D global SEM matrix associated to ad operator -nu u'' + beta u'
0003 %
0004 %    [A]=ad_1d_se(npdx,ne,nov,nu,beta,wx,dx,jacx); produces the matrix
0005 %
0006 %        A_{ij}=(nu phi_j', phi'_i)_N +beta( phi_j' ,phi_i)_N of size
0007 %
0008 %        (noe,noe) where noe=nov(npdx,ne) is the number of d.o.f.
0009 %
0010 % Input : npdx = polynomial degree in every element
0011 %         ne = number of spectral elements
0012 %         nov = local -global map, previously generated by cosnov1d
0013 %         nu   = viscosity (constant>0)
0014 %         beta = coefficient of first order term (constant)
0015 %         wx = npdx LGL weigths in [-1,1],
0016 %            (produced by calling [x,w]=xwlgl(npdx))
0017 %            (npdx = number of nodes, =n+1, if n=polynomial degree)
0018 %         dx = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
0019 %         jacx =  jacobian of the map F:[-1,1]---->[xa_ie,b_ie]
0020 %
0021 % Output: A = matrix (noe,noe)
0022 %
0023 %
0024 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0025 %                    "Spectral Methods. Fundamentals in Single Domains"
0026 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0027 
0028 %   Written by Paola Gervasio
0029 %   $Date: 2007/04/01$
0030 
0031 noe=nov(npdx,ne);
0032 A=sparse(noe,noe);
0033 for ie=1:ne
0034 Al=ad_1d_sp(nu,beta,wx,dx,jacx(ie));
0035 A(nov(1:npdx,ie),nov(1:npdx,ie))=A(nov(1:npdx,ie),nov(1:npdx,ie))+Al;
0036 end
0037 
0038