stiffq1H

 STIFFQ1H Construction of stiffness Q1 matrix on the coarse grid.
 
 [Ac,Acb,wwc,lista_coarse,noec,novc,lintc,ldirc]=...
   stiffq1H(nx,nex,ny,ney,xy,nov,ifro);

   called by schwarz_2d.m and b eig_schwarz_2d.m

 Input:  
        nx = polynomial degree in each element (the same in each element)
               along x-direction
        nex = number of elements (equally spaced) along x-direction
        ny = polynomial degree in each element (the same in each element)
               along y-direction%        gammax = column or row array of length nex-1. 
        ney = number of elements (equally spaced) along y-direction
        xy = column array with global mesh, length: noe=nov(npdx*npdy,ne)
        nov = local -global map, previously generated by cosnov_2d
        ifro = column array of length noe=nov(npdx*npdy,ne):
            if (x_i,y_i) is internal to Omega then ifro(i)=0,
            if (x_i,y_i) is on \partial\Omega then ifro(i)=1,

 Output:
        Ac =  Cholesky factor of the Q1 stiffness matrix (internal/internal nodes) 
               on the coarse mesh
        Acb = Q1 stiffness matrix (internal/boundary nodes) 
               on the coarse mesh
        wwc = Q1 mass matrix (internal nodes) 
                on the coarse mesh
        lista_coarse = list of nodes of Omega wich are nodes of teh coarse mesh
        noec = number of nodes of the coarse mesh
        novc(4,ne) = it maps each macro-Q1 element on the coarse mesh Q1
        lintc = lista of internal nodes of the coarse mesh
        ldirc = lista of boudanry nodes of the coarse mesh

 References: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
                    "Spectral Methods. Fundamentals in Single Domains"
                    Springer Verlag, Berlin Heidelberg New York, 2006.
             CHQZ3 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
                    "Spectral Methods. Evolution to Complex Geometries 
                     and Applications to Fluid DynamicsSpectral Methods"
                    Springer Verlag, Berlin Heidelberg New York, 2007.

0001 function [Ac,Acb,wwc,lista_coarse,noec,novc,lintc,ldirc]=...
0002     stiffq1H(nx,nex,ny,ney,xy,nov,ifro);
0003 % STIFFQ1H Construction of stiffness Q1 matrix on the coarse grid.
0004 %
0005 % [Ac,Acb,wwc,lista_coarse,noec,novc,lintc,ldirc]=...
0006 %   stiffq1H(nx,nex,ny,ney,xy,nov,ifro);
0007 %
0008 %   called by schwarz_2d.m and b eig_schwarz_2d.m
0009 %
0010 % Input:
0011 %        nx = polynomial degree in each element (the same in each element)
0012 %               along x-direction
0013 %        nex = number of elements (equally spaced) along x-direction
0014 %        ny = polynomial degree in each element (the same in each element)
0015 %               along y-direction%        gammax = column or row array of length nex-1.
0016 %        ney = number of elements (equally spaced) along y-direction
0017 %        xy = column array with global mesh, length: noe=nov(npdx*npdy,ne)
0018 %        nov = local -global map, previously generated by cosnov_2d
0019 %        ifro = column array of length noe=nov(npdx*npdy,ne):
0020 %            if (x_i,y_i) is internal to Omega then ifro(i)=0,
0021 %            if (x_i,y_i) is on \partial\Omega then ifro(i)=1,
0022 %
0023 % Output:
0024 %        Ac =  Cholesky factor of the Q1 stiffness matrix (internal/internal nodes)
0025 %               on the coarse mesh
0026 %        Acb = Q1 stiffness matrix (internal/boundary nodes)
0027 %               on the coarse mesh
0028 %        wwc = Q1 mass matrix (internal nodes)
0029 %                on the coarse mesh
0030 %        lista_coarse = list of nodes of Omega wich are nodes of teh coarse mesh
0031 %        noec = number of nodes of the coarse mesh
0032 %        novc(4,ne) = it maps each macro-Q1 element on the coarse mesh Q1
0033 %        lintc = lista of internal nodes of the coarse mesh
0034 %        ldirc = lista of boudanry nodes of the coarse mesh
0035 %
0036 % References: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0037 %                    "Spectral Methods. Fundamentals in Single Domains"
0038 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0039 %             CHQZ3 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0040 %                    "Spectral Methods. Evolution to Complex Geometries
0041 %                     and Applications to Fluid DynamicsSpectral Methods"
0042 %                    Springer Verlag, Berlin Heidelberg New York, 2007.
0043 
0044 %   Written by Paola Gervasio
0045 %   $Date: 2007/04/01$
0046 
0047 npdx=nx+1;npdy=ny+1;ne=nex*ney;
0048 npxc=nex+1;npyc=ney+1;noec=npxc*npyc;
0049 mn=npdx*npdy;nm1=mn-npdx+1;
0050 
0051 % costruisco la mesh coarse
0052 [lista_coarse,novc,novcg,jacxe,jacye]=meshq1_coarse(npdx,npdy,nov,xy);
0053 noec=length(lista_coarse);
0054 
0055 xyc=zeros(noec,2); xyc(:,1)=xy(lista_coarse,1);xyc(:,2)=xy(lista_coarse,2);
0056 ifroc=zeros(noec,1); ifroc=ifro(lista_coarse);
0057 
0058 x=[-1;1]; wx=[1;1]; dx=[-0.5,0.5;-0.5,0.5];
0059 y=x;wy=wx;dy=dx;
0060 iparl=zeros(10,1);
0061 iparl(7)=noec;iparl(6)=ne;iparl(1)=2;iparl(2)=2;iparl(3)=4;
0062 
0063 
0064 
0065 % costruisco la matrice Q1 del laplaciano sull'elemento esteso.
0066 [Ac,wwc]=stiffq1_se(iparl,ifroc,novc,wx,dx,jacxe,wy,dy,jacye);
0067 
0068 % filtro la matrice sui nodi interni e sui nodi di bordo
0069 % e costruisco la fattorizzazione di Cholesky di Al
0070 
0071  [ldirc,lintc]=liste1(ifroc);
0072  Acb=Ac(lintc,ldirc);
0073  Ac=Ac(lintc,lintc);
0074  wwc=wwc(lintc);
0075  Ac=chol(Ac);
0076  
0077  return