CG vs AMG

December 5, 2003, 08:26

what are the relative advantages/disadvantages and applications of the Conjugate gradient vs the advanced multi grid solvers. I have had a flick through the methadology manual but it seems a little vague

December 7, 2003, 08:15

On grids that have the major flow in one direction, say in a pipe, or where one needs a lot of pressure sweeps, I've had decrease in solution time by an order of magnitude using the amg solver. I have not noticed any difference in the 'converged' solution between the amg/cg solvers in the cases I've run.

Allan

December 8, 2003, 02:23

I've compared the amg solver in a case resembling well a pipe flow case and the speed up was about 1.9 compared to the cg solver. However, sometimes the amg solver may produce some oscillations to the solution. So caution is needed.

December 31, 2003, 05:37

Just a quick precision: CG means Conjugate Gradient. It is an iterative solver family based on the Krylov subspace method (see also Golub & Van Loan, "Matrix computations", 1996) and is a good "smoother", which means that the smoothes the higher frequencies of the error quite rapidly. The idea is to use successive coarser meshes, on which the lower frequencies of the error on the fine mesh become the high ones on the coarser meshes. The error level can be then reduced very rapidly on the coarse meshes. As it is difficult to construct geometrically coarser meshes, one idea is to use the coefficients of the matrices to solve to provide a coarsening algorithm. This is what the AMG (Algebraic MultiGrid) solver does and this is why the AMG solver brings you the computational time down. Small drawback: You need more memory because of the coarsening strategy.

December 5, 2003, 08:26	CG vs AMG	#1
Joel Guest Posts: n/a	what are the relative advantages/disadvantages and applications of the Conjugate gradient vs the advanced multi grid solvers. I have had a flick through the methadology manual but it seems a little vague

December 7, 2003, 08:15	Re: CG vs AMG	#2
allan Guest Posts: n/a	On grids that have the major flow in one direction, say in a pipe, or where one needs a lot of pressure sweeps, I've had decrease in solution time by an order of magnitude using the amg solver. I have not noticed any difference in the 'converged' solution between the amg/cg solvers in the cases I've run. Allan

December 8, 2003, 02:23	Re: CG vs AMG	#3
Ossi Guest Posts: n/a	I've compared the amg solver in a case resembling well a pipe flow case and the speed up was about 1.9 compared to the cg solver. However, sometimes the amg solver may produce some oscillations to the solution. So caution is needed.

December 31, 2003, 05:37	Re: CG vs AMG	#4
4xF Guest Posts: n/a	Just a quick precision: CG means Conjugate Gradient. It is an iterative solver family based on the Krylov subspace method (see also Golub & Van Loan, "Matrix computations", 1996) and is a good "smoother", which means that the smoothes the higher frequencies of the error quite rapidly. The idea is to use successive coarser meshes, on which the lower frequencies of the error on the fine mesh become the high ones on the coarser meshes. The error level can be then reduced very rapidly on the coarse meshes. As it is difficult to construct geometrically coarser meshes, one idea is to use the coefficients of the matrices to solve to provide a coarsening algorithm. This is what the AMG (Algebraic MultiGrid) solver does and this is why the AMG solver brings you the computational time down. Small drawback: You need more memory because of the coarsening strategy.