function CreateGradBasisFunction(iscale,nmod)
load(fullfile('TMP','params'));
param0=param;
inde=[];
tic;
load(fullfile('TMP',sprintf('%d_params',nmod)),'param');
pscale=2^(iscale-1);
sbasis=param.basis;
if strcmp(sbasis,'nurbs')&&iscale>1
sbasis='fem';
end
switch sbasis
case 'KM'
load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
wdetJ=1;
ind=param.km_indices;
kappa=param.kolosov;
modes=param.modes;
if isfield(param,'crack_id')
ic=param.crack_id;
else
ic=1;
end
load(fullfile('TMP',sprintf('%d_mask_%d',nmod,iscale-1)),'mask');
sizemask=numel(mask);
if sizemask==1
ipix=[];
else
ipix=find(diag(mask)>0);
end
[dkmdx,dkmdy]=CreateGradKMBasis(modes,ind,kappa,ipix,ic);
epsxx=real(dkmdx);
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,(iscale-1))),'epsxx','wdetJ','sizeim');
epsyy=imag(dkmdy);
save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,(iscale-1))),'epsyy','sizeim');
epsxy=imag(dkmdx)+real(dkmdy);
save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,(iscale-1))),'epsxy','sizeim');
% [km]=CreateKMBasis(modes,ind,kappa,[]);
%
%
%
%
% [kmy,kmx]=gradient(reshape(real(km(:,1)),sizeim));
% kmx=kmx.*reshape(diag(mask),sizeim);
% kmy=kmy.*reshape(diag(mask),sizeim);
% figure
% toto=reshape(real(dkmdx(:,1)),sizeim);
% imagesc(toto(2:sizeim(1)-1,2:sizeim(2)-1))
% colorbar;
% figure
% imagesc(kmx(2:sizeim(1)-1,2:sizeim(2)-1))
% colorbar;
% figure
% imagesc(abs(kmx(2:sizeim(1)-1,2:sizeim(2)-1)-toto(2:sizeim(1)-1,2:sizeim(2)-1)))
% colorbar;
case 'KM+'
load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
wdetJ=1;
ind=[0,2];
kappa=param.kolosov;
modes=param.modes;
lmin=param.cz_length;
if isfield(param,'crack_id')
ic=param.crack_id;
else
ic=1;
end
load(fullfile('TMP',sprintf('%d_mask_%d',nmod,iscale-1)),'mask');
sizemask=numel(mask);
if sizemask==1
ipix=[];
else
ipix=find(diag(mask)>0);
end
load(fullfile('TMP',sprintf('%d_iphi_%d',nmod,iscale-1)),'iphi','ztip','dz');
epsxx=[];epsxy=[];epsyy=[];
if any(modes==1)
for iz=1:length(ztip)
[dkmdx,dkmdy]=CreateGradKMBasis(1,1,kappa,ipix,ic,ztip(iz));
epsxx=[epsxx,real(dkmdx)*dz(iz)];
epsyy=[epsyy,imag(dkmdy)*dz(iz)];
epsxy=[epsxy,imag(dkmdx)*dz(iz)+real(dkmdy)*dz(iz)];
end
end
if any(modes==2)
for iz=1:length(ztip)
[dkmdx,dkmdy]=CreateGradKMBasis(2,1,kappa,ipix,ic,ztip(iz));
epsxx=[epsxx,real(dkmdx)*dz(iz)];
epsyy=[epsyy,imag(dkmdy)*dz(iz)];
epsxy=[epsxy,imag(dkmdx)*dz(iz)+real(dkmdy)*dz(iz)];
end
end
if length(modes)==2
iphi=blkdiag(iphi,iphi);
end
epsxx=epsxx*iphi;
epsyy=epsyy*iphi;
epsxy=epsxy*iphi;
[dkmdx,dkmdy]=CreateGradKMBasis([1,2],ind,kappa,ipix,ic);
epsxx=[real(dkmdx),epsxx];
epsyy=[imag(dkmdy),epsyy];
epsxy=[imag(dkmdx)+real(dkmdy),epsxy];
% if any(modes==2)
% [dkmdx,dkmdy]=CreateGradKMBasis(2,1,kappa,ipix,ic);
%
% epsxx=[epsxx,real(dkmdx)];
% epsyy=[epsyy,imag(dkmdy)];
% epsxy=[epsxy,imag(dkmdx)+real(dkmdy)];
%
% end
if isfield(param,'sub_indices')
sind=param.sub_indices;
if ~isempty(sind)
[dkmdx,dkmdy]=CreateGradKMBasis(modes,sind,kappa,ipix,ic,lmin);
epsxx=[epsxx,real(dkmdx)];
epsyy=[epsyy,imag(dkmdy)];
epsxy=[epsxy,imag(dkmdx)+real(dkmdy)];
end
end
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,(iscale-1))),'epsxx','wdetJ','sizeim');
save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,(iscale-1))),'epsyy','sizeim');
save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,(iscale-1))),'epsxy','sizeim');
% case 'sfem'
%
% load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
% mesh_file=fullfile('TMP',sprintf('%d_mesh_%d',nmod,iscale-1));
% load(fullfile('TMP',sprintf('%d_mask_%d',nmod,iscale-1)),'unmasked_nodes');
% [dphidx,dphidy]=CreateGradSmoothFiniteElementBasis(mesh_file,sizeim,pscale,unmasked_nodes,'Gauss_points');
% phi0=sparse(size(dphidx,1),size(dphidx,2));
% epsxx=[dphidx,phi0];
% save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,10*(iscale-1))),'epsxx','sizeim');
% epsyy=[phi0,dphidy];
% save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,10*(iscale-1))),'epsyy','sizeim');
% epsxy=[dphidy,dphidx];
% save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,10*(iscale-1))),'epsxy','sizeim');
case 'fem'
load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
mesh_file=fullfile('TMP',sprintf('%d_mesh_%d',nmod,iscale-1));
load(fullfile('TMP',sprintf('%d_mask_%d',nmod,iscale-1)),'cut_nodes','unmasked_nodes');
[dphidx,dphidy]=CreateGradFiniteElementBasis(mesh_file,sizeim,pscale,unmasked_nodes,'Gauss_points');
[wdetJ,inde]=GetWeigthDetJ(mesh_file,sizeim,1,'Gauss_points');
if (~isempty(cut_nodes))
[dphidxp,dphidyp]=CreateGradFiniteElementBasis(mesh_file,sizeim,pscale,cut_nodes,'pixels',1);
wdetJp=GetWeigthDetJ(mesh_file,sizeim,1,'pixels');
wdetJ=[wdetJ*ones(size(dphidx,2),1);wdetJp*ones(size(dphidxp,2),1)];
wdetJ=diag(sparse(wdetJ));
dphidx=[dphidx;dphidxp(:,unmasked_nodes)];
dphidy=[dphidy;dphidyp(:,unmasked_nodes)];
end
phi0=sparse(size(dphidx,1),size(dphidx,2));
epsxx=[dphidx,phi0];
Uxx=[dphidx,phi0];
Uxy=[dphidy,phi0];
Uyx=[phi0,dphidx];
Uyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,10*(iscale-1))),'Uxx','epsxx','wdetJ','sizeim');
epsyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,10*(iscale-1))),'Uyy','epsyy','sizeim');
epsxy=[dphidy,dphidx];
save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,10*(iscale-1))),'Uyx','Uxy','epsxy','sizeim');
case 'nurbs'
load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
p=param.degree;
mesh_file=fullfile('TMP',sprintf('%d_mesh_%d',nmod,iscale-1));
[dphidx,dphidy,Xi,Yi,wdetJ]=CreateGradNURBSBasis(mesh_file,p,'Gauss_points',1,'physical');
phi0=sparse(size(dphidx,1),size(dphidx,2));
epsxx=[dphidx,phi0];
Uxx=[dphidx,phi0];
Uxy=[dphidy,phi0];
Uyx=[phi0,dphidx];
Uyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,10*(iscale-1))),'Uxx','epsxx','wdetJ','Xi','Yi','sizeim');
epsyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,10*(iscale-1))),'Uyy','epsyy','sizeim');
epsxy=[dphidy,dphidx];
save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,10*(iscale-1))),'Uyx','Uxy','epsxy','sizeim');
[dphidxx,dphidyy,dphidxy,xg,yg,wdetJ]=CreateGradGradNURBSBasis(mesh_file,p,'Gauss_points',1,'physical');
phi0=sparse(size(dphidxx,1),size(dphidxx,2));
epsxxx=[dphidxx,phi0];
epsxxy=[dphidxy,phi0];
epsyyy=[phi0,dphidyy];
epsyyx=[phi0,dphidxy];
epsxyx=[dphidxy,dphidxx];
epsxyy=[dphidyy,dphidxy];
save(fullfile('TMP',sprintf('%d_epsijk_%d',nmod,10*(iscale-1))),'epsxxx','epsxxy','epsxyx','epsxyy','epsyyx','epsyyy');
case 'btri'
load(fullfile('TMP',sprintf('sample0_%d',iscale-1)),'sizeim');
mesh_file=fullfile('TMP',sprintf('%d_mesh_%d',nmod,iscale-1));
[phi,Xi,Yi,wdetJ]=CreateBezierTriangleBasis(mesh_file,'Gauss_points');
[dphidx,dphidy,wdetJ]=CreateGradBezierTriangleBasis(mesh_file,'Gauss_points');
phi0=sparse(size(dphidx,1),size(dphidx,2));
epsxx=[dphidx,phi0];
Uxx=[dphidx,phi0];
Uxy=[dphidy,phi0];
Uyx=[phi0,dphidx];
Uyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,10*(iscale-1))),'Uxx','epsxx','wdetJ','sizeim');
epsyy=[phi0,dphidy];
save(fullfile('TMP',sprintf('%d_epsyy_%d',nmod,10*(iscale-1))),'Uyy','epsyy','sizeim');
epsxy=[dphidy,dphidx];
save(fullfile('TMP',sprintf('%d_epsxy_%d',nmod,10*(iscale-1))),'Uyx','Uxy','epsxy','sizeim');
otherwise
error ('INVALID FUNCTIONAL BASIS');
end
if (iscale==1)&&(isfield(param,'enrichment'))
if isfield(param,'mesh_size_ratio')
assert(param.mesh_size_ratio==1);
end
enr=param.enrichment;
mesh_file=fullfile('TMP',sprintf('%d_meshx_%d',nmod,iscale-1));
load(mesh_file,'ng','Nelems');
wdetJ=GetWeigthDetJ(mesh_file,sizeim,1,'sub_cells',1);
npt=size(wdetJ,1);
if npt==1
npt=prod(sizeim);
end
epsxx=sparse(npt,size(epsxx,2));
epsyy=sparse(npt,size(epsxx,2));
epsxy=sparse(npt,size(epsxx,2));
Uxy=sparse(npt,size(epsxx,2));
Uyx=sparse(npt,size(epsxx,2));
epscxx=sparse(npt,size(epsxx,2));
epscyy=sparse(npt,size(epsxx,2));
epscxy=sparse(npt,size(epsxx,2));
Ucxy=sparse(npt,size(epsxx,2));
Ucyx=sparse(npt,size(epsxx,2));
if ~iscell(param0.levelset_file)
nbfis=1;
else
nbfis=numel(param0.levelset_file);
end
wdetJ=0*wdetJ;
for ic=1:nbfis
load(fullfile('TMP',sprintf('%d_enrichment_%d',nmod,ic)),'enriched_nodes','enriched_elts','tip_nodes','face_nodes','enriched_pixels');
wdetJi=GetWeigthDetJ(mesh_file,sizeim,1,'sub_cells',enriched_elts);
wdetJ=wdetJ+wdetJi;
phi=CreateFiniteElementBasis(mesh_file,sizeim,pscale,enriched_nodes,'sub_cells',true);
load(mesh_file,'xo','yo');
xp=phi*xo;yp=phi*yo;
% figure
% imagesc(reshape(sum(phi,2),sizeim))
% figure
% plot(sum(phi,2))
% % any(sum(phi,2)>1)
% figure
% scatter(xp,yp,1+sum(phi,2))
%
% figure
% plot(xo,yo,'b+')
% hold on
% plot(xp,yp,'ko')
% axis xy
% axis image
% pause
[dphidx,dphidy]=CreateGradFiniteElementBasis(mesh_file,sizeim,pscale,enriched_nodes,'sub_cells',true);
if isempty(unmasked_nodes)
phi0=sparse(size(phi,1),size(phi,2));
epscxx=epscxx+[dphidx,phi0];
epscyy=epscyy+[phi0,dphidy];
epscxy=epscxy+[dphidy,dphidx];
Ucxy=Ucxy+[dphidy,phi0];
Ucyx=Ucyx+[phi0,dphidx];
else
phi0=sparse(size(phi,1),length(unmasked_nodes));
epscxx=epscxx+[dphidx(:,unmasked_nodes),phi0];
epscyy=epscyy+[phi0,dphidy(:,unmasked_nodes)];
epscxy=epscxy+[dphidy(:,unmasked_nodes),dphidx(:,unmasked_nodes)];
Ucxy=Ucxy+[dphidy(:,unmasked_nodes),phi0];
Ucyx=Ucyx+[phi0,dphidx(:,unmasked_nodes)];
end
do_disc_enrich=true;
if ~(strcmp(enr,'crack_disc'))
ind=param.km_indices;
kappa=param.kolosov;
modes=param.modes;
[dkmdx,dkmdy]=CreateGradKMBasis(modes,ind,kappa,enriched_pixels,ic);
[km]=CreateKMBasis(modes,ind,kappa,enriched_pixels,ic);
strat=param.enrichment_type;
if isempty(face_nodes)
do_disc_enrich=false;
end
if isempty(enriched_pixels)&&strcmp(strat,'zone')
phikm=1;
dphikmdx=0;
dphikmdy=0;
else
phikm=phi(:,tip_nodes);
dphikmdx=dphidx(:,tip_nodes);
dphikmdy=dphidy(:,tip_nodes);
if strcmp(strat,'zone')
phikm=sum(phikm,2);
dphikmdx=sum(dphikmdx,2);
dphikmdy=sum(dphikmdy,2);
end
% if strcmp(strat,'zone')
% load(fullfile('TMP',sprintf('%d_cutoff_%d',nmod,iscale-1),'cutoff','dcdx','dcdy');
% phikm=cutoff;
% dphikmdx=dcdx;
% dphikmdy=dcdy;
% clear cutoff dcdx dcdy
% else
% phikm=phi(:,tip_nodes);
% dphikmdx=dphidx(:,tip_nodes);
% dphikmdy=dphidy(:,tip_nodes);
% end
end
if strcmp(strat,'zone')
epsxx=[epsxx,diag(sparse(phikm))*real(dkmdx)+diag(sparse(dphikmdx))*real(km)];
epsyy=[epsyy,diag(sparse(phikm))*imag(dkmdy)+diag(sparse(dphikmdy))*imag(km)];
epsxy=[epsxy,diag(sparse(phikm))*(real(dkmdy)+imag(dkmdx))+diag(sparse(dphikmdy))*real(km)+diag(sparse(dphikmdx))*imag(km)];
Uxy=[Uxy,diag(sparse(phikm))*(real(dkmdy))+diag(sparse(dphikmdy))*real(km)];
Uyx=[Uyx,diag(sparse(phikm))*(imag(dkmdx))+diag(sparse(dphikmdx))*imag(km)];
elseif strcmp(strat,'node')
for kk=1:size(km,2)
epsxx= [epsxx,diag(sparse(real(dkmdx(:,kk))))*phikm+diag(sparse(real(km(:,kk))))*dphikmdx];
epsyy= [epsyy,diag(sparse(imag(dkmdy(:,kk))))*phikm+diag(sparse(imag(km(:,kk))))*dphikmdy];
epsxy= [epsxy,diag(sparse(real(dkmdy(:,kk))+imag(dkmdx(:,kk))))*phikm+diag(sparse(imag(km(:,kk))))*dphikmdx+diag(sparse(real(km(:,kk))))*dphikmdy];
Uxy=[Uxy,diag(sparse(phikm))*(real(dkmdy(:,kk)))+diag(sparse(dphikmdy))*real(km(:,kk))];
Uyx=[Uyx,diag(sparse(phikm))*(imag(dkmdx(:,kk)))+diag(sparse(dphikmdx))*imag(km(:,kk))];
end
end
clear km dkmdx dkmdy dphikmdx dphikmdy
end
if do_disc_enrich
load(fullfile('TMP',sprintf('%d_levelsets',ic)),'crack');
if isfield(param,'shift_enrichment')
opti_shift=param.shift_enrichment;
else
opti_shift=0;
end
if ~opti_shift
crack=interp2(crack,yp,xp,'*linear');
heaviside=2*double(crack>=0)-1;
% crack=crack(enriched_pixels);
% heaviside=zeros(prod(sizeim),1);
% heaviside(enriched_pixels)=2*double(crack>=0)-1;
% figure
% imagesc(full(reshape(heaviside,sizeim)))
% figure
% scatter(xp,yp,10+0*yp,heaviside)
% hold on
% plot(xo,yo,'+','MarkerSize',10,'LineWidth',2)
% figure
% scatter(xp,yp,10+0*yp,sum(abs(dphidx),2))
% face_nodes
% figure
% scatter(xp,yp,10+0*yp,sum(abs(dphidx(:,face_nodes)),2))
clear crack
heaviside=diag(sparse(heaviside));
dphihdx=heaviside*dphidx(:,face_nodes);
dphihdy=heaviside*dphidy(:,face_nodes);
else
disp('WARNING SHIFTED ENRICHMENT !!!');
load(mesh_file,'xo','yo');
hn=interp2(crack,yo,xo,'*linear');
hn=double(hn>=0);
hn=diag(sparse(hn(face_nodes)));
% crack=crack(enriched_pixels);
% heaviside=zeros(prod(sizeim),1);
% heaviside(enriched_pixels)=double(crack>=0);
crack=interp2(crack,yp,xp,'*linear');
heaviside=double(crack>=0);
% figure
% imagesc(reshape(heaviside,sizeim)')
% hold on
% plot(xo,yo,'ko')
% axis xy
% axis image
% axis off;
clear crack
heaviside=diag(sparse(heaviside));
dphihdx=heaviside*dphidx(:,face_nodes)-dphidx(:,face_nodes)*hn;
dphihdy=heaviside*dphidy(:,face_nodes)-dphidy(:,face_nodes)*hn;
end
phih0=sparse(size(dphihdx,1),size(dphihdx,2));
epsxx=[epsxx,dphihdx,phih0];
epsyy=[epsyy,phih0,dphihdy];
epsxy=[epsxy,dphihdy,dphihdx];
Uxy=[Uxy,dphihdy,phih0];
Uyx=[Uyx,phih0,dphihdx];
clear dphidx dphidy phih0 heaviside
end
end
eps0=sparse(npt,size(epsxx,2)-size(epscxx,2));
epscxx=[epscxx,eps0];
epscyy=[epscyy,eps0];
epscxy=[epscxy,eps0];
Ucxy=[Ucxy,eps0];
Ucyx=[Ucyx,eps0];
epsxx=epscxx+epsxx;
epsyy=epscyy+epsyy;
epsxy=epscxy+epsxy;
Uxy=Ucxy+Uxy;
Uyx=Ucyx+Uyx;
save(fullfile('TMP',sprintf('%d_xepsxx_%d',nmod,(iscale-1))),'epsxx','wdetJ','inde','sizeim');
save(fullfile('TMP',sprintf('%d_xepsyy_%d',nmod,(iscale-1))),'epsyy','sizeim');
save(fullfile('TMP',sprintf('%d_xepsxy_%d',nmod,(iscale-1))),'Uxy','Uyx','epsxy','sizeim');
end
Nddl_tot=size(epsxx,2);
% disp(sprintf('Creating gradient basis function for model %d...%6.2f s',nmod,toc));
save(fullfile('TMP',sprintf('%d_epsxx_%d',nmod,10*(iscale-1))),'Nddl_tot','-append');
end
