Preconditioner Details

mchurchf · March 14, 2012, 14:51

Can someone please point me toward a reference that describes the diagonal incomplete Cholesky preconditioning used in OpenFOAM? It would be much appreciated. What I don't understand is the "diagonal" part. What exactly does that mean?

Thank you,

Matt

ingcorra · August 21, 2013, 10:35

Hi! Did you find anything useful meanwhile? I'm facing the same problem... I don't understand what exactly 'diagonal-based' means. Thanks

cfdonline2mohsen · August 24, 2013, 15:34

Dear Foamers
Have a look at the following references for more details (especially the Jacob report 1980):

P. K. Khosla, and S. G. Rubin, “A diagonally dominant second-order accurate implicit scheme”, Computers and Fluids, 2:207-209, 1974.

M. R. Hestens, and E. L. Steifel, “Method of conjugate gradients for solving
linear systems”, Journal of Research, 29:409-436, 1952.

D. A. H. Jacobs, “Preconditioned Conjugate Gradient methods for solving
systems of algebraic equations”, Central Electricity Research Laboratories
Report, RD/L/N193/80, 1980.

H. A. Van Der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems”, SIAM J. Scientific Computing, 13(2):631-644, 1992.

immortality · August 25, 2013, 05:45

whats the differences between preconditioners and smoothers?
is there some references about DICGaussSeidel and/or DILUGaussSeidel?
what about solver "smoothSolver"?

March 14, 2012, 14:51	Preconditioner Details	#1
mchurchf Member Matthew J. Churchfield Join Date: Nov 2009 Location: Boulder, Colorado, USA Posts: 49 Rep Power: 18	Can someone please point me toward a reference that describes the diagonal incomplete Cholesky preconditioning used in OpenFOAM? It would be much appreciated. What I don't understand is the "diagonal" part. What exactly does that mean? Thank you, Matt

August 24, 2013, 15:34		#3
cfdonline2mohsen Senior Member Mohsen KiaMansouri Join Date: Jan 2010 Location: CFD Lab Posts: 118 Rep Power: 16	Dear Foamers Have a look at the following references for more details (especially the Jacob report 1980): P. K. Khosla, and S. G. Rubin, “A diagonally dominant second-order accurate implicit scheme”, Computers and Fluids, 2:207-209, 1974. M. R. Hestens, and E. L. Steifel, “Method of conjugate gradients for solving linear systems”, Journal of Research, 29:409-436, 1952. D. A. H. Jacobs, “Preconditioned Conjugate Gradient methods for solving systems of algebraic equations”, Central Electricity Research Laboratories Report, RD/L/N193/80, 1980. H. A. Van Der Vorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems”, SIAM J. Scientific Computing, 13(2):631-644, 1992. hua1015, immortality and ingcorra like this. __________________ “If you have an apple and I have an apple and we exchange these apples then you and I will still each have one apple. But if you have an idea and I have an idea and we exchange these ideas, then each of us will have two ideas.”

August 25, 2013, 05:45		#4
immortality Senior Member Ehsan Join Date: Oct 2012 Location: Iran Posts: 2,208 Rep Power: 26	whats the differences between preconditioners and smoothers? is there some references about DICGaussSeidel and/or DILUGaussSeidel? what about solver "smoothSolver"? divyaa likes this. __________________ Injustice Anywhere is a Threat for Justice Everywhere.Martin Luther King. To Be or Not To Be,Thats the Question! The Only Stupid Question Is the One that Goes Unasked.

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August 21, 2013, 10:35		#2
ingcorra New Member My Name Join Date: Jan 2013 Posts: 13 Rep Power: 13	Hi! Did you find anything useful meanwhile? I'm facing the same problem... I don't understand what exactly 'diagonal-based' means. Thanks