adr_1d_sp

 ADR_1D_SP Computes 1D local spectral matrix associated to adr operator -(nu u' + b(x) u)'+gam u

          advection-diffusion-raction operator (one spectral element)

  [A]=adr_1d_sp(wx,dx,jacx,nu,b,gam) produces the matrix 

 Input:
      A_{ij}=(nu phi_j' + b phi_j, phi'_i)_N +(gam phi_j,phi_i)_N

      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]
      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)

 Output: A = matrix (npdx,npdx) defined above


 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_sp(wx,dx,jacx,nu,b,gam)
0002 % ADR_1D_SP Computes 1D local spectral matrix associated to adr operator -(nu u' + b(x) u)'+gam u
0003 %
0004 %          advection-diffusion-raction operator (one spectral element)
0005 %
0006 %  [A]=adr_1d_sp(wx,dx,jacx,nu,b,gam) produces the matrix
0007 %
0008 % Input:
0009 %      A_{ij}=(nu phi_j' + b phi_j, phi'_i)_N +(gam phi_j,phi_i)_N
0010 %
0011 %      wx = npdx LGL weigths in [-1,1],
0012 %          (produced by calling [x,w]=xwlgl(npdx))
0013 %          (npdx = number of nodes, =n+1, if n=polynomial degree)
0014 %      dx = first derivative LGL matrix (produced by calling d=derlgl(x,npdx))
0015 %      jacx =  jacobian of the map F:[-1,1]---->[xa_ie,b_ie]
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 %
0021 % Output: A = matrix (npdx,npdx) defined above
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   coef1=nu/jacx; coef2=gam*jacx;
0032   A=dx'*(diag(wx)*(coef1*dx+diag(b)))+coef2*diag(wx);
0033