GMRES Setup

andreasp · October 22, 2012, 04:47

Dear CFD community,

we are using a stabilized first order Finite Element code for simulation of incompressible flows. At its core, the code utilizes a (usually non-preconditioned) GMRES method for solving linear systems.

In general, it is quite difficult to find an "ideal" setup of the GMRES algorithm for a given problem, i.e. especially to find a suitable size of the maximum Krylov space dimension (inner iterations). I wonder if there are any estimates for determining such parameters beforehand, in order to circumvent some of the trial and error procedure (which is really cumbersome and painful for large problems). Maybe someone can point me to literature where such an issue might be discussed....?

Thanks for any help!
Andreas

cdegroot · October 23, 2012, 15:43

Nice post. I've looked into this in the past, but also found no suitable answer. I'd be interested to know what others have to say. I actually found for the linear systems I was using GMRES wasn't a great choice and found better convergence using a TFQMR solver. I'm sure that is not a general result though, just a property of the linear systems I was constructing.

October 22, 2012, 04:47	GMRES Setup	#1
andreasp New Member Andreas P Join Date: Sep 2010 Posts: 26 Rep Power: 15	Dear CFD community, we are using a stabilized first order Finite Element code for simulation of incompressible flows. At its core, the code utilizes a (usually non-preconditioned) GMRES method for solving linear systems. In general, it is quite difficult to find an "ideal" setup of the GMRES algorithm for a given problem, i.e. especially to find a suitable size of the maximum Krylov space dimension (inner iterations). I wonder if there are any estimates for determining such parameters beforehand, in order to circumvent some of the trial and error procedure (which is really cumbersome and painful for large problems). Maybe someone can point me to literature where such an issue might be discussed....? Thanks for any help! Andreas

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October 23, 2012, 15:43		#2
cdegroot Senior Member Chris DeGroot Join Date: Nov 2011 Location: Canada Posts: 414 Rep Power: 17	Nice post. I've looked into this in the past, but also found no suitable answer. I'd be interested to know what others have to say. I actually found for the linear systems I was using GMRES wasn't a great choice and found better convergence using a TFQMR solver. I'm sure that is not a general result though, just a property of the linear systems I was constructing.