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BICGSTABIter_p.m
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function [p_int] = BICGSTABIter_p(u,r,Nr,Np,hr,hp,f)
%ip = Nr-1 ; jp = Np/2 ;
STOP = false ;
BICGEPS = 1.0e-16 ;
Temp=ComputeAX_p(u,r,Nr,Np,hr,hp) ;
% Initial vector r_0 = b - Ax_0, and r0* = r_0
for i = 2:(Nr-1)
for j =1:Np
Uj(i,j) = u(i,j) ;
rj(i,j) = f(i,j) - Temp(i,j) ;
r0_star(i,j) = rj(i,j) ;
%{
if (i == ip) && (j == jp)
Uj(i,j) = 0.0 ;
rj(i,j) = 0.0 ;
r0_star(i,j) = 0.0 ;
end
%}
end
end
BICG_ITER = 0 ; norm = 0.0 ;
while ((BICG_ITER < 10000 ) && (~STOP == 1))
% compute rhoj = (r0, r0*)
rhoj = 0.0 ;
for i = 2:(Nr-1)
for j =1:Np
rhoj = rhoj + rj(i,j)*r0_star(i,j) ;
end
end
if ( sqrt(rhoj/((Nr-1)*(Np+1))) < BICGEPS )
STOP = true ;
else
if ( BICG_ITER == 0 )
for i = 2:(Nr-1)
for j = 1:Np
pj(i,j) = rj(i,j); % p0 = r0
end
end
else
betaj = (rhoj/rhoj_Minus)*(alphaj/omegaj) ;
for i = 1:(Nr-1)
for j = 1:Np
pj(i,j) = rj(i,j) + betaj*(pj(i,j) - omegaj*Var(i,j));
end
end
end
%Solve for Upstar, Vpstar from Ku* = u...., where K is the preconditioning matrix
for i = 2:(Nr-1)
for j = 1:Np
% No preconditioning
pstar(i,j) = pj(i,j) ;
end
end
% compute vj = A*pstar
for i = 2:(Nr-1)
for j = 1:Np
%{
if (i == ip) && (j == jp)
u(i,j) = 0.0 ;
else
u(i,j) = pstar(i,j) ;
end
%}
u(i,j) = pstar(i,j) ;
end
end
Temp=ComputeAX_p(u,r,Nr,Np,hr,hp) ;
for i = 2:(Nr-1)
for j = 1:Np
Var(i,j) = Temp(i,j) ;
end
end
H1 = 0.0 ;
for i = 2:(Nr-1)
for j = 1:Np
H1 = H1 + Var(i,j)*r0_star(i,j) ;
end
end
alphaj = rhoj/H1 ;
% find sj
for i = 2:(Nr-1)
for j = 1:Np
sj(i,j) = rj(i,j) - alphaj*Var(i,j) ;
end
end
% Solve for Upstar, Vpstar from Ku* = u...., where K is the preconditioning matrix
for i = 2:(Nr-1)
for j = 1:Np
% No preconditioning
sstar(i,j) = sj(i,j) ;
end
end
norm = 0.0 ;
for i = 2:(Nr-1)
for j = 1:Np
norm = norm + sstar(i,j)*sstar(i,j) ;
end
end
norm = sqrt(norm/((Nr-1)*(Np+1))) ;
if( norm < BICGEPS)
STOP = true ; % if ||s||_2 is small x_i = x_{i-1} + alphai*p_i
for i = 2:(Nr-1)
for j = 1:Np
%{
if (i == ip) && (j == jp)
Uj(i,j) = 0.0 ;
else
Uj(i,j) = Uj(i,j)+ alphaj*pstar(i,j) ;
end
%}
Uj(i,j) = Uj(i,j)+ alphaj*pstar(i,j) ;
end
end
else
% compute t = As
for i = 2:(Nr-1)
for j = 1:Np
%{
if (i == ip) && (j == jp)
u(i,j) = 0.0 ;
else
u(i,j) = sstar(i,j) ;
end
%}
u(i,j) = sstar(i,j) ;
end
end
Temp=ComputeAX_p(u,r,Nr,Np,hr,hp) ;
H1 = 0.0 ; H2 = 0.0 ;
for i = 2:(Nr-1)
for j = 1:Np
H1 = H1 + Temp(i,j)*sj(i,j) ;
H2 = H2 + Temp(i,j)*Temp(i,j) ;
end
end
omegaj = H1/H2;
% find xj
norm = 0.0 ;
for i = 2:(Nr-1)
for j = 1:Np
H1 = (alphaj*pstar(i,j) + omegaj*sstar(i,j)) ;
%{
if (i == ip) && (j == jp)
Uj(i,j) = 0.0 ;
else
Uj(i,j) = Uj(i,j) + H1 ;
end
%}
Uj(i,j) = Uj(i,j) + H1 ;
norm = norm + H1*H1 ;
end
end
norm = sqrt(norm/((Nr-1)*(Np+1))) ;
if(norm < BICGEPS)
STOP = true ;
end
% find rjplusone
for i = 2:(Nr-1)
for j = 1:Np
rj(i,j) = sj(i,j) - omegaj*Temp(i,j);
end
end
rhoj_Minus = rhoj ;
end
end
BICG_ITER = BICG_ITER + 1 ;
end
for i = 2:(Nr-1)
for j = 1:Np
p_int(i,j) = Uj(i,j) ;
end
end
fprintf('\n Pressure converged at Iter %d, ', BICG_ITER);
end