SCHUR_ASSEMB Assembles global Schur complement matrix
Input: AGG =structure of local matrices A_{\Gamma_m,\Gamma_m}
Amm = structure of local matrices (A_{m,m})^{-1}
AGm = structure of local matrices A_{\Gamma_m,m}
Lmm = structure containing maps from internal{\Omega_m to \Omega_m
set in schur_local.m
LGG = structure with maps from \Gamma_i to \Gamma
set in schur_local.m
novi = 2-indexes array of size (max(nvli),ne), computed in cosnovi
nvli = column array. nvli(ie) is the number of nodes of \Omega_ie
internal to Omega.
nov = 2-index array of local to global map,
size(nov)=[max(npdx*npdy),ne]
novg = restriction map from (\cup_i \Omega_i) to \Gamma
set in cosnovg.m
lint = list of those nodes of Omega (close) which
are internal to Omega.
lgamma = list of internal nodes which are on the interface between
spectral elements
ugamma = u on the interface Gamma
f = r.h.s.
ub = solution on \partial\Omega
Output: un = solution in Omega
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 [Sigma]=schur_assemb(AGG,Amm,AGm,LGG,novg,... 0002 lint,lgamma,param); 0003 % SCHUR_ASSEMB Assembles global Schur complement matrix 0004 % 0005 % Input: AGG =structure of local matrices A_{\Gamma_m,\Gamma_m} 0006 % Amm = structure of local matrices (A_{m,m})^{-1} 0007 % AGm = structure of local matrices A_{\Gamma_m,m} 0008 % Lmm = structure containing maps from internal{\Omega_m to \Omega_m 0009 % set in schur_local.m 0010 % LGG = structure with maps from \Gamma_i to \Gamma 0011 % set in schur_local.m 0012 % novi = 2-indexes array of size (max(nvli),ne), computed in cosnovi 0013 % nvli = column array. nvli(ie) is the number of nodes of \Omega_ie 0014 % internal to Omega. 0015 % nov = 2-index array of local to global map, 0016 % size(nov)=[max(npdx*npdy),ne] 0017 % novg = restriction map from (\cup_i \Omega_i) to \Gamma 0018 % set in cosnovg.m 0019 % lint = list of those nodes of Omega (close) which 0020 % are internal to Omega. 0021 % lgamma = list of internal nodes which are on the interface between 0022 % spectral elements 0023 % ugamma = u on the interface Gamma 0024 % f = r.h.s. 0025 % ub = solution on \partial\Omega 0026 % 0027 % Output: un = solution in Omega 0028 % 0029 % 0030 % References: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0031 % "Spectral Methods. Fundamentals in Single Domains" 0032 % Springer Verlag, Berlin Heidelberg New York, 2006. 0033 % CHQZ3 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0034 % "Spectral Methods. Evolution to Complex Geometries 0035 % and Applications to Fluid DynamicsSpectral Methods" 0036 % Springer Verlag, Berlin Heidelberg New York, 2007. 0037 0038 % Written by Paola Gervasio 0039 % $Date: 2007/04/01$ 0040 0041 0042 n=length(lgamma); 0043 [ldnov,ne]=size(novg); 0044 Sigma=zeros(n,n); 0045 0046 % Schur complement 0047 for ie=1:ne 0048 lg=LGG{ie}; 0049 ngammam=length(lg); 0050 agg=AGG{ie};agm=AGm{ie};amm=Amm{ie}; 0051 Sigma_ie=agg-agm*amm*agm'; 0052 Sigma(novg(lg,ie),novg(lg,ie))=Sigma(novg(lg,ie),novg(lg,ie))+Sigma_ie; 0053 end 0054 0055 if(param(1)==2) 0056 % (Neumann Neumann preconditioner) 0057 for ie=1:ne 0058 lg=LGG{ie}; 0059 ngammam=length(lg); 0060 agg=AGG{ie};agm=AGm{ie};amm=Amm{ie}; 0061 Sigma_ie=agg-agm*amm*agm'; 0062 Sigma(novg(lg,ie),novg(lg,ie))=Sigma(novg(lg,ie),novg(lg,ie))+Sigma_ie; 0063 end 0064 end 0065 0066 return