adr_1d_se

 ADR_1D_SE Assembles 1D global spectral element matrix associated to adr operator -(nu u' + b(x) u)'+gam u

   advection-diffusion-raction operator   -(nu u' + b(x) u)'+gam u


    [A]=adr_1d_se(npdx,ne,nov,nu,b,gam,wx,dx,jacx); produces the matrix

        A_{ij}=(nu (phi_j)' + b phi_j, (phi_i)') +(gam phi_j,phi_i) 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)
         b = column vector with evaluation of b(x) at LGL node of the spectral
          element
         gam  = coefficient of zeroth order term (constant>0)
         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]=adr_1d_se(npdx,ne,nov,nu,b,gam,wx,dx,jacx);
0002 % ADR_1D_SE Assembles 1D global spectral element matrix associated to adr operator -(nu u' + b(x) u)'+gam u
0003 %
0004 %   advection-diffusion-raction operator   -(nu u' + b(x) u)'+gam u
0005 %
0006 %
0007 %    [A]=adr_1d_se(npdx,ne,nov,nu,b,gam,wx,dx,jacx); produces the matrix
0008 %
0009 %        A_{ij}=(nu (phi_j)' + b phi_j, (phi_i)') +(gam phi_j,phi_i) of size
0010 %
0011 %        (noe,noe) where noe=nov(npdx,ne) is the number of d.o.f.
0012 %
0013 % Input : npdx = polynomial degree in every element
0014 %         ne = number of spectral elements
0015 %         nov = local -global map, previously generated by cosnov1d
0016 %         nu   = viscosity (constant>0)
0017 %         b = column vector with evaluation of b(x) at LGL node of the spectral
0018 %          element
0019 %         gam  = coefficient of zeroth order term (constant>0)
0020 %         wx = npdx LGL weigths in [-1,1],
0021 %            (produced by calling [x,w]=xwlgl(npdx))
0022 %            (npdx = number of nodes, =n+1, if n=polynomial degree)
0023 %         dx = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
0024 %         jacx =  jacobian of the map F:[-1,1]---->[xa_ie,b_ie]
0025 %
0026 % Output: A = matrix (noe,noe)
0027 %
0028 %
0029 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0030 %                    "Spectral Methods. Fundamentals in Single Domains"
0031 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0032 
0033 %   Written by Paola Gervasio
0034 %   $Date: 2007/04/01$
0035 
0036 noe=nov(npdx,ne);
0037 A=sparse(noe,noe);
0038 for ie=1:ne
0039 Al=adr_1d_sp(wx,dx,jacx(ie),nu,b(nov(1:npdx,ie)),gam);
0040 A(nov(1:npdx,ie),nov(1:npdx,ie))=A(nov(1:npdx,ie),nov(1:npdx,ie))+Al;
0041 end
0042 
0043