partition

 PARTITION Computes the diagonal weighting matrix D relative to interface unknowns

 [D]=partition(Rgamma)

  Computes the diagonal weighting matrix D relative to the interface
  unknowns: 
  D_ii=1/n_i   where n_i is the number of subdomains x_i belongs to.
  (see CHQZ3, pag. 397)

 Input : Rgamma = matrix contructed in cosrgam.m

 Output : D, column array of size ngamma (global number of interface nodes)

 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 [D]=partition(Rgamma)
0002 % PARTITION Computes the diagonal weighting matrix D relative to interface unknowns
0003 %
0004 % [D]=partition(Rgamma)
0005 %
0006 %  Computes the diagonal weighting matrix D relative to the interface
0007 %  unknowns:
0008 %  D_ii=1/n_i   where n_i is the number of subdomains x_i belongs to.
0009 %  (see CHQZ3, pag. 397)
0010 %
0011 % Input : Rgamma = matrix contructed in cosrgam.m
0012 %
0013 % Output : D, column array of size ngamma (global number of interface nodes)
0014 %
0015 % References: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0016 %                    "Spectral Methods. Fundamentals in Single Domains"
0017 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0018 %             CHQZ3 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0019 %                    "Spectral Methods. Evolution to Complex Geometries
0020 %                     and Applications to Fluid DynamicsSpectral Methods"
0021 %                    Springer Verlag, Berlin Heidelberg New York, 2007.
0022 
0023 %   Written by Paola Gervasio
0024 %   $Date: 2007/04/01$
0025 
0026 
0027 
0028 [ne,ngamma]=size(Rgamma);
0029 D=zeros(ngamma,1);
0030 for i=1:ngamma
0031 D(i)=max(Rgamma(:,i));
0032 end