COSNOVENEW Construction of restriction maps for extended elements
[nove,nvle]=cosnovenew(npdx,nex,npdy,ney,nov,ifro,nlevel);
Input: nx = polynomial degree in each spectral element along x-direction
nex = number of spectral elements along x-direction
ny = polynomial degree in each spectral element along y-direction
ney = number of spectral elements along y-direction
nov = 2-index array of local to global map,
size(nov)=[max(npdx*npdy),ne]
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,
nlevel = number of added layers for extending spectral elements
inside additive Schwarz preconditioner.
If param(2)==1, the preconditioner is P^{m}_{as,H}
(minimum overlap), pag. 377 CHQZ3)
If param(2)==2, the preconditioner is P^{s}_{as,H}
(small overlap), pag. 377 CHQZ3)
param(2) is a positive integer less than min(nx,ny)
Output: nove = 2-index array of "extended local" to global map,
nvle = 2-index array:
nvle (:,1)=number of nodes of the extendend elements
nvle (:,2)=number of Q1 elements of the extendend elements
along x-direction
nvle (:,3)=number of Q1 elements of the extendend elements
along y-direction
References: 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 [nove,nvle]=cosnovenew(nx,nex,ny,ney,nov,ifro,nlevel); 0002 % COSNOVENEW Construction of restriction maps for extended elements 0003 % 0004 % [nove,nvle]=cosnovenew(npdx,nex,npdy,ney,nov,ifro,nlevel); 0005 % 0006 % Input: nx = polynomial degree in each spectral element along x-direction 0007 % nex = number of spectral elements along x-direction 0008 % ny = polynomial degree in each spectral element along y-direction 0009 % ney = number of spectral elements along y-direction 0010 % nov = 2-index array of local to global map, 0011 % size(nov)=[max(npdx*npdy),ne] 0012 % ifro = column array of length noe=nov(npdx*npdy,ne): 0013 % if (x_i,y_i) is internal to Omega then ifro(i)=0, 0014 % if (x_i,y_i) is on \partial\Omega then ifro(i)=1, 0015 % nlevel = number of added layers for extending spectral elements 0016 % inside additive Schwarz preconditioner. 0017 % If param(2)==1, the preconditioner is P^{m}_{as,H} 0018 % (minimum overlap), pag. 377 CHQZ3) 0019 % If param(2)==2, the preconditioner is P^{s}_{as,H} 0020 % (small overlap), pag. 377 CHQZ3) 0021 % param(2) is a positive integer less than min(nx,ny) 0022 % 0023 % Output: nove = 2-index array of "extended local" to global map, 0024 % nvle = 2-index array: 0025 % nvle (:,1)=number of nodes of the extendend elements 0026 % nvle (:,2)=number of Q1 elements of the extendend elements 0027 % along x-direction 0028 % nvle (:,3)=number of Q1 elements of the extendend elements 0029 % along y-direction 0030 % 0031 % 0032 % References: CHQZ3 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, 0033 % "Spectral Methods. Evolution to Complex Geometries 0034 % and Applications to Fluid DynamicsSpectral Methods" 0035 % Springer Verlag, Berlin Heidelberg New York, 2007. 0036 0037 % Written by Paola Gervasio 0038 % $Date: 2007/04/01$ 0039 0040 [ldnov,ne]=size(nov); 0041 0042 npdx=nx+1; npdy=ny+1;mn=npdx*npdy; 0043 nm1=mn-nx; 0044 mne=(npdx+nlevel*2)*(npdy+nlevel*2); 0045 nove=zeros(mne,ne); 0046 nvle=zeros(ne,3); 0047 for ie=1:ne 0048 nove(1:mn,ie)=nov(1:mn,ie); 0049 nvle(ie,2)=nx; nvle(ie,3)=ny; 0050 ultimo=mn; 0051 vertex=zeros(4,1); 0052 0053 % vertex 1 0054 0055 ig=nov(1,ie); 0056 if(ifro(ig)<=0) 0057 vertex(1)=1; 0058 % The vertex is inside Omega, I expand nov 0059 % by adding the last "nlevel" rows of the domain down 0060 for ib=1:nlevel 0061 nove(ultimo+1:ultimo+npdx,ie)=nov(npdx*(ny-ib)+1:npdx*(ny-ib+1),ie-1); 0062 ultimo=ultimo+npdx; nvle(ie,3)=nvle(ie,3)+1; 0063 end 0064 0065 % by adding the last "nlevel" columns of the left domain 0066 for ib=1:nlevel 0067 nove(ultimo+1:ultimo+npdy,ie)=nov(nx-ib+1:npdx:mn-ib,ie-ney); 0068 ultimo=ultimo+npdy; nvle(ie,2)=nvle(ie,2)+1; 0069 end 0070 % by adding nodes of the element symmetric to "ie" with respect to the vertex 0071 for ib=1:nlevel 0072 nove(ultimo+1:ultimo+nlevel,ie)=nov(mn-npdx*ib-nlevel:mn-npdx*ib-1,ie-ney-1); 0073 ultimo=ultimo+nlevel; 0074 end 0075 end 0076 0077 % vertex 2 0078 0079 ig=nov(npdx,ie); 0080 if(ifro(ig)<=0) 0081 vertex(2)=1; 0082 % The vertex is inside Omega, I expand nov 0083 if vertex(1)==0 0084 % by adding the last "nlevel" rows of the domain down 0085 for ib=1:nlevel 0086 nove(ultimo+1:ultimo+npdx,ie)=nov(npdx*(ny-ib)+1:npdx*(ny-ib+1),ie-1); 0087 ultimo=ultimo+npdx;nvle(ie,3)=nvle(ie,3)+1; 0088 end 0089 end 0090 % by adding the first "nlevel" columns of the right domain 0091 for ib=1:nlevel 0092 nove(ultimo+1:ultimo+npdy,ie)=nov(ib+1:npdx:nm1+ib,ie+ney); 0093 ultimo=ultimo+npdy; nvle(ie,2)=nvle(ie,2)+1; 0094 end 0095 % by adding nodes of the element symmetric to "ie" with respect to the vertex 0096 for ib=1:nlevel 0097 nove(ultimo+1:ultimo+nlevel,ie)=nov(mn-npdx*(ib+1)+2:mn-npdx*(ib+1)+1+nlevel,ie+ney-1); 0098 ultimo=ultimo+nlevel; 0099 end 0100 end 0101 0102 % vertex 3 0103 0104 ig=nov(mn,ie); 0105 if(ifro(ig)<=0) 0106 vertex(3)=1; 0107 % The vertex is inside Omega, I expand nov 0108 if vertex(2)==0 0109 % by adding the first "nlevel" columns of the right domain 0110 for ib=1:nlevel 0111 nove(ultimo+1:ultimo+npdy,ie)=nov(ib+1:npdx:nm1+ib,ie+ney); 0112 ultimo=ultimo+npdy; nvle(ie,2)=nvle(ie,2)+1; 0113 end 0114 end 0115 % by adding the last "nlevel" rows of the domain up 0116 for ib=1:nlevel 0117 nove(ultimo+1:ultimo+npdx,ie)=nov(npdx*ib+1:npdx*(ib+1),ie+1); 0118 ultimo=ultimo+npdx; nvle(ie,3)=nvle(ie,3)+1; 0119 end 0120 % by adding nodes of the element symmetric to "ie" with respect to the vertex 0121 for ib=1:nlevel 0122 nove(ultimo+1:ultimo+nlevel,ie)=nov(npdx*ib+2:npdx*ib+1+nlevel,ie+ney+1); 0123 ultimo=ultimo+nlevel; 0124 end 0125 end 0126 0127 % vertex 4 0128 0129 ig=nov(nm1,ie); 0130 if(ifro(ig)<=0) 0131 vertex(4)=1; 0132 % The vertex is inside Omega, I expand nov 0133 if vertex(1)==0 0134 % by adding the last "nlevel" columns of the left domain 0135 for ib=1:nlevel 0136 nove(ultimo+1:ultimo+npdy,ie)=nov(nx-ib+1:npdx:mn-ib,ie-ney); 0137 ultimo=ultimo+npdy; nvle(ie,2)=nvle(ie,2)+1; 0138 end 0139 end 0140 if vertex(3)==0 0141 % by adding the last "nlevel" rows of the domain up 0142 for ib=1:nlevel 0143 nove(ultimo+1:ultimo+npdx,ie)=nov(npdx*ib+1:npdx*(ib+1),ie+1); 0144 ultimo=ultimo+npdx; nvle(ie,3)=nvle(ie,3)+1; 0145 end 0146 end 0147 % by adding nodes of the element symmetric to "ie" with respect to the vertex 0148 for ib=1:nlevel 0149 nove(ultimo+1:ultimo+nlevel,ie)=nov(npdx*(ib+1)-nlevel:npdx*(ib+1)-1,ie-ney+1); 0150 ultimo=ultimo+nlevel; 0151 end 0152 end 0153 nvle(ie,1)=ultimo; 0154 0155 end % end loop ie