Convergence Acceleration
 

Dear friends,

I have a question may be very common in CFD, I'm coding a program to solve Boussinesq Equation for water waves. I use Adams-Bashforth scheme to do the time integeration. Firstly using an explicit predictor and then using an implicit corrector which is iterated till the convergence criteria is satisfied.

Now I need about 6~10 iteration steps to converge, is it feasible? Below is a typical output(eps=1E-6 as convergence criteria):

c-----------------------------

it= 4959 iter= 1 error= 8.43487059E-05

it= 4959 iter= 2 error= 2.88610408E-05

it= 4959 iter= 3 error= 1.94194149E-05

it= 4959 iter= 4 error= 1.62095684E-05

it= 4959 iter= 5 error= 1.39913941E-05

it= 4959 iter= 6 error= 1.23509949E-05

it= 4959 iter= 7 error= 1.10735346E-05

it= 4959 iter= 8 error= 1.00386389E-05

it= 4959 iter= 9 error= 9.17477037E-06

c----------------------------

My question is, as you can see that in the first two or three iteration steps, the error goes down quickly, but then after 4 steps, the convergence rate becomes somehow slowly. I want the code to converge in 4~5 steps to save more time. Any one can point me a way to accelerate the convergence using information of the previous iteration steps?

Thanks in advance,

Wen Long

Re: Convergence Acceleration
 

Acceleration techniques: (i) Multigrid (ii)Preconditioning (iii)GMRES(Generalized Minimum Residual)

These are some of the methods to accelerate the convergence....

Re: Convergence Acceleration
 

net-boltzmann method dns and so on