mesh_1d

 MESH_1D   Generates uniform 1D Spectral elements mesh

  [xx,xy,jacx,ww]=mesh_1d(xa,xb,ne,npdx,nov,x,wx)

 Input: xa,xb= extrema of computational domain Omega=(xa,xb)
        ne = number of elements
        npdx = number of nodes in each element (the same in every element)
        nov = local -global map, previously generated by cosnov1d
        x = LGL nodes in [-1,1], previously generated by xwlgl
        wx = LGL weigths in [-1,1], previously generated by xwlgl

 Output: xx = 2-indexes array of size (2,ne): xx(1:2,ie)=[xa_ie;xb_ie]
         jacx = array (length(jacx)=ne); jacx(ie)= jacobian of 
                of the map F_ie:[-1,1]---->[xa_ie,xb_ie]
         xy = column array with global mesh, length: noe=nov(npdx,ne)
         ww = column array with global weigths, length: noe=nov(npdx,ne)
              diag(ww) is the mass matrix associated to SEM discretization

 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[xx,jacx,xy,ww]=mesh_1d(xa,xb,ne,npdx,nov,x,wx)
0002 % MESH_1D   Generates uniform 1D Spectral elements mesh
0003 %
0004 %  [xx,xy,jacx,ww]=mesh_1d(xa,xb,ne,npdx,nov,x,wx)
0005 %
0006 % Input: xa,xb= extrema of computational domain Omega=(xa,xb)
0007 %        ne = number of elements
0008 %        npdx = number of nodes in each element (the same in every element)
0009 %        nov = local -global map, previously generated by cosnov1d
0010 %        x = LGL nodes in [-1,1], previously generated by xwlgl
0011 %        wx = LGL weigths in [-1,1], previously generated by xwlgl
0012 %
0013 % Output: xx = 2-indexes array of size (2,ne): xx(1:2,ie)=[xa_ie;xb_ie]
0014 %         jacx = array (length(jacx)=ne); jacx(ie)= jacobian of
0015 %                of the map F_ie:[-1,1]---->[xa_ie,xb_ie]
0016 %         xy = column array with global mesh, length: noe=nov(npdx,ne)
0017 %         ww = column array with global weigths, length: noe=nov(npdx,ne)
0018 %              diag(ww) is the mass matrix associated to SEM discretization
0019 %
0020 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0021 %                    "Spectral Methods. Fundamentals in Single Domains"
0022 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0023 
0024 %   Written by Paola Gervasio
0025 %   $Date: 2007/04/01$
0026 
0027 noe=nov(npdx,ne);
0028 
0029 xy=zeros(noe,1); ww=zeros(noe,1); jacx=zeros(ne,1);
0030 xx=zeros(2,ne);
0031 H=(xb-xa)/ne;
0032 for ie=1:ne
0033 xb_ie=xa+ie*H;
0034 xa_ie=xb_ie-H;
0035 xx(1:2,ie)=[xa_ie;xb_ie];
0036 jacx(ie)=.5*(xb_ie-xa_ie);
0037 for i=1:npdx
0038 xy(nov(i,ie))=x(i)*jacx(ie)+.5*(xb_ie+xa_ie);
0039 ww(nov(i,ie))=ww(nov(i,ie))+wx(i)*jacx(ie);
0040 end
0041 end
0042 
0043