hi all,

It is obvious that when we discretise Navier-Stokes equations with central differencing scheme, the resulting matrix will be of penta-diagonal. There are number of special solvers to handle this like Stones algorithm and its variants, Krylov solver etc. Which has the fastest convergence rate among all these solver types from your experience?

thanks for your reply...

I assume that you are talking about implicit algorithms.There are two ways to handle the penta diagonal solver.One is the direct inversion of the pentadiagonal system.The other possible way is to use the approximate factorization to split it into two tridiagonal systems which are much faster to invert than the pentadiagonal system.

Or you could use Gauss-Seidel or another iterative approach.

Also uncoupled and two space dimensions?

hi otd, yes. I am dealing with uncoupled 2D flows only.. I know there are number of iterative schemes to solve penta diagonal matrix.. I need to know which of these has fastest convergence rate.. thanks

Do you mean, for a given precision e, which algorithm can solve the pentadiagonal fastest?

I think multigrid should be the fastest for this type of problem. ILU/GS will eventually stagnate when the low wave number component of residual is dominant. I've seen somewhere that multigrid+SIP(strongly implicit) is pretty good.

One question, is it positive definite? If so preconditioning CG should be very effective.

Actually the best, and quickest, method of solving this is by considering the pentadiagonal system as a tridiagonal system whose entries are 2x2 matrices. The resulting block tridiagonal system can be solved using a variant of the standard tridiagonal solver.

thank you friends.. I will look at CG and multi-gird methods.. If you get to know more details regarding this, kindly post a reply..

Before talking about improvements, you need to look for appropriate methods depending on the matrix properties. You can see in this link a very good introductory in this matter :

http://netlib2.cs.utk.edu/linalg/htm...Templates.html

When a method is working, no matter how long it takes, then you can look for preconditionners.