### Email Archive: libmesh-users (read-only)

 Re: [Libmesh-users] Algebraic multigrid From: Travis Austin - 2007-03-01 21:33 ```Hi Roy,=0A=0AThe nonlinear Navier-Stokes equation is a difficult problem. = It is nonsymmetric =0Aand with strong convection can create a mess. Much r= esearch has gone into solving =0Athis problem using AMG as well as many oth= er solvers and if you are interested you =0Acould find a number of papers o= n what is required of AMG to work well.=0A=0AAMG was originally defined for= symmetric positive definite problems and once you=0Aget outside of that re= alm you should take a look at what others have done. I have=0Aa colleague = who has done work on Navier-Stokes and MG and I'm waiting for his=0Aopinion= . Is it possible to try regular multigrid on this problem and if so how do= es=0Ait perform? Just curious.=0A=0ACheers, Travis=0A=0A----- Original Mes= sage ----=0AFrom: Roy Stogner Please= note that you must have a recent version of petsc (2.3.x) that is=0A> comp= iled with HYPRE support. Earlier versions of petsc do not make room=0A> fo= r HYPRE use.=0A=0AI note that one probably should also have a more intimate= knowledge of=0AHYPRE than I do - on the first complicated example problem = I tried (3D=0Alid-driven cavity incompressible flow), the linear symmetric = Stokes=0Aflow case was unbelievably faster using multigrid, but as soon as = I=0Aturn on the nonlinear/nonsymmetric Navier-Stokes convection term,=0Asom= ething goes wrong. The KSP residuals say I'm converged, but Newton=0Adoesn= 't think that the result is even necessarily a descent direction.=0A---=0AR= oy=0A=0A-------------------------------------------------------------------= ------=0ATake Surveys. Earn Cash. Influence the Future of IT=0AJoin SourceF= orge.net's Techsay panel and you'll get the chance to share your=0Aopinions= on IT & business topics through brief surveys-and earn cash=0Ahttp://www.t= echsay.com/default.php?page=3Djoin.php&p=3Dsourceforge&CID=3DDEVDEV=0A_____= __________________________________________=0ALibmesh-users mailing list=0AL= ibmesh-users@... href="0Ahttps://lists.sourceforge.net/lists/li=" target="_new">0Ahttps://lists.sourceforge.net/lists/li= stinfo/libmesh-users=0A=0A=0A=0A=0A=0A=0A=0A =0A___________________________= _________________________________________________________=0AFinding fabulou= s fares is fun. =0ALet Yahoo! FareChase search your favorite travel sites = to find flight and hotel bargains.=0Ahttp://farechase.yahoo.com/promo-gener= ic-14795097 ```

 Re: [Libmesh-users] Algebraic multigrid From: Roy Stogner - 2007-03-01 21:57 ```On Thu, 1 Mar 2007, Travis Austin wrote: > The nonlinear Navier-Stokes equation is a difficult problem. It is > nonsymmetric and with strong convection can create a mess. That's what we're finding. An undergraduate student here has a weakly-coupled microfluidics problem with Reynolds number 0.01, which BoomerAMG handles fine, but Peclet number 10, which makes BoomerAMG explode. In other words, weak nonlinearities are fine, but even the linear convection-diffusion equation fails when the convection is turned up enough. His diverged result looks somewhat similar to a coarse grid Galerkin solution, as if that cell Peclet number is too high and the solution is overwhelmed by coarse node to coarse node oscillations. We're going to play around with limiting the number of multigrid levels, on the theory that we'll be fine so long as the coarsest grid isn't too coarse to be stable. But he knows even less about multigrid than I do, so nobody's getting their hopes up. I think the best solution may be to use a stabilized formulation instead of Galerkin, but that's not an option for us at the moment. > Is it possible to try regular multigrid on this problem and if so > how does it perform? Just curious. Not unless someone's added geometric multigrid capabilities but just hasn't committed the changes to CVS yet. ;-) It's a shame BoomerAMG isn't more tightly integrated into PETSc. It would be nice to play around with smoothers and coarse grid solvers other than weighted Jacobi, SOR, and Gaussian. I'd like to try something like ILU4 on the coarse grid combined with ILU0 on finer grids, and see what that does for some of my problems. --- Roy ```
 Re: [Libmesh-users] Algebraic multigrid From: Travis Austin - 2007-03-01 22:29 Attachments: Message as HTML ```Roy,=0A=0AFirst, I assume that you are using GMRES as the main solver with = AMG as the=0Apreconditioner. Second, what type of discretization are you u= sing because from=0Amy understanding that can affect accuracy and also the = resulting solver? Are you=0Ausing an upwinding approach that takes into ac= count the direction of convection?=0A=0AI believe that this is an active ar= ea of research and new theses are churning out=0Aat the moment. One paper = that I just found can be downloaded as below=0A=0Ahttp://www.cs.umd.edu/~el= man/papers/mg-amg-paper.pdf=0A=0AYou can use many command line options with= AMG to set different parameters but=0Ayou'll need to look through petsc co= de or documentation to find these options. I'd=0Aalso suggest looking at p= apers (like the one above) for proper AMG parameters. =0A=0ACheers, Travis= =0A=0A----- Original Message ----=0AFrom: Roy Stogner =0ATo: Travis Austin The nonlinear Navier-Stokes equation is a difficult problem. It= is=0A> nonsymmetric and with strong convection can create a mess.=0A=0ATha= t's what we're finding. An undergraduate student here has a=0Aweakly-coupl= ed microfluidics problem with Reynolds number 0.01, which=0ABoomerAMG handl= es fine, but Peclet number 10, which makes BoomerAMG=0Aexplode. In other w= ords, weak nonlinearities are fine, but even the=0Alinear convection-diffus= ion equation fails when the convection is=0Aturned up enough.=0A=0AHis dive= rged result looks somewhat similar to a coarse grid Galerkin=0Asolution, as= if that cell Peclet number is too high and the solution=0Ais overwhelmed b= y coarse node to coarse node oscillations. We're=0Agoing to play around wi= th limiting the number of multigrid levels, on=0Athe theory that we'll be f= ine so long as the coarsest grid isn't too=0Acoarse to be stable. But he k= nows even less about multigrid than I do,=0Aso nobody's getting their hopes= up.=0A=0AI think the best solution may be to use a stabilized formulation= =0Ainstead of Galerkin, but that's not an option for us at the moment.=0A= =0A> Is it possible to try regular multigrid on this problem and if so=0A> = how does it perform? Just curious.=0A=0ANot unless someone's added geometr= ic multigrid capabilities but just=0Ahasn't committed the changes to CVS ye= t. ;-)=0A=0AIt's a shame BoomerAMG isn't more tightly integrated into PETS= c. It=0Awould be nice to play around with smoothers and coarse grid solver= s=0Aother than weighted Jacobi, SOR, and Gaussian. I'd like to try=0Asomet= hing like ILU4 on the coarse grid combined with ILU0 on finer=0Agrids, and = see what that does for some of my problems.=0A---=0ARoy=0A=0A--------------= -----------------------------------------------------------=0ATake Surveys.= Earn Cash. Influence the Future of IT=0AJoin SourceForge.net's Techsay pan= el and you'll get the chance to share your=0Aopinions on IT & business topi= cs through brief surveys-and earn cash=0Ahttp://www.techsay.com/default.php= ?page=3Djoin.php&p=3Dsourceforge&CID=3DDEVDEV=0A___________________________= ____________________=0ALibmesh-users mailing list=0ALibmesh-users@...= rceforge.net=0Ahttps://lists.sourceforge.net/lists/listinfo/libmesh-users= =0A=0A=0A=0A=0A=0A=0A=0A =0A_______________________________________________= _____________________________________=0ADo you Yahoo!?=0AEveryone is raving= about the all-new Yahoo! Mail beta.=0Ahttp://new.mail.yahoo.com ```
 Re: [Libmesh-users] Algebraic multigrid From: Roy Stogner - 2007-03-05 18:32 ```On Thu, 1 Mar 2007, Travis Austin wrote: > First, I assume that you are using GMRES as the main solver with AMG > as the reconditioner. Yes. > Second, what type of discretization are you using because from my > understanding that can affect accuracy and also the resulting > solver? Velocity-pressure formulation, biquadratic/bilinear mixed elements, both adaptive and uniform quad meshes. > Are you using an upwinding approach that takes into account the > direction of convection? No. Like I said (although I think I called it "stabilization" instead of upwinding), this looks a bit like the problem we're seeing. The exact solution of the non-stabilized equations is good on the fine grid, but oscillatory on the coarse grid and on the diverged multigrid solution. On the other hand, a proper stabilization term should disappear as the grid becomes fine enough - otherwise you're just adding numerical diffusion to the system and you're no longer solving the same problem. For geometric multigrid, I can see how an unstabilized operator on the coarse grid would ruin convergence... but with algebraic multigrid, I'd expect the "auto-generated" coarse system to effecively have a subgrid stabilization term built in. What's new is that his code now seems to work (at least up to Pe=10) when he goes straight for the fine grid solution - it seems that before he refining one level at a time, using projected coarse grid solutions as fine grid starting iterates. I'm not sure whether it's really working or whether it's just seeming to, though - at low Re I get incorrect Newton steps that can "trick" the nonlinear solver into stepsize-criterion convergence even when the nonlinear residual is still much higher than I'd like. > I believe that this is an active area of research and new theses are > churning out at the moment. One paper that I just found can be > downloaded as below > http://www.cs.umd.edu/~elman/papers/mg-amg-paper.pdf They're adding a element size-dependent numerical diffusion to the system to stabilize it. I'll see if I can pick out any more differences on a closer read. Thanks! --- Roy ```