Biconjugate gradient stabilized method
From CFD-Wiki
Biconjugate gradient stabilized method
Biconjugate gradient stabilized method could be summarized as follows
System of equation
For the given system of equation
Ax = b ;
b = source vector
x = solution variable for which we seek the solution
A = coefficient matrix
M = the precondioning matrix constructued by matrix A
Algorithm
Allocate temperary vectors p, phat, s, shat, t, v, rtilde
Allocate temerary reals rho_1, rho_2 , alpha, beta, omega
r := b - Ax
rtilde = r
for i := 1 step 1 until max_itr do rho_1 = rtilder
if i = 1 then p := r else
beta = (rho_1/rho_2) * (alpha/omega)
p = r + beta * (p - omega * v)
end if
solve (Mphat = p )
v = Aphat
alpha = rho_1 / (rtildev)
s = r - alpha * v
solve (Mshat = s )
t = A * shat; omega = (ts) / (tt)
x = x + alpha * phat + omega * shat
r = s - omega * t
rho_2 = rho_1
end (i-loop) deallocate all temp memory
return TRUE