>> Can you write me the exact expression of the problem you're solving?
The example I forwarded you earlier by Benjamin Kirk solves the Laplace-Young problem. I have linked a paper by C.F. Scott et al on "Computation of capillary surfaces for the Laplace-Young equation". This should help whoever is interested in knowing the exact system that the code solves for. (http://eprints.maths.ox.ac.uk/304/01/QJMAM0416.pdf as of 01/31/08) Matrix free technique: Yes, Knoll's paper is a fantastic introduction to obtain a good grasp on JFNK technique. I would recommend that to anyone who wants to solve nonlinear problems in a matrix free way. Let me rewrite the expression you wrote as J*v = (F(u+epsilon*v)-F(u)) / epsilon Where epsilon is a small perturbation and F(u) is the nonlinear residual function and J is the jacobian matrix of the nonlinear system. The above formula compute the action of a Jacobian on a given vector, or more specifically the Krylov vector if you are using say GMRES or CG to solve your system. F(u) is the right hand side because the Newton linearization yields the system J*delu = -residual = -F(u) But since the whole point is not to form the matrix J, you could just find the action of the matrix on a vector to build the Krylov subspace and solve the system. Hope that helps. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of li pan Sent: Thursday, January 31, 2008 8:05 AM To: Vijay S. Mahadevan Cc: [email protected] Subject: Re: [Libmesh-users] matrix free scheme thanx a lot! Can you write me the exact expression of the problem you're solving? Recently, I read the paper of Knoll about JFNK method (Jacobian-free NewtonKrylov methods: a survey of approaches and applications). I'm not sure whether I understood well. Please correct me. If r_0 is the first residual, J is the jacobian matrix, In the approximation J*r_0 = (F(u+\epsilon r_0)-F(u)) / \epsilon F(u) is the residual, right? But in Knoll's paper F(u) seems the right hand side. Or I am wrong. pan --- "Vijay S. Mahadevan" <[EMAIL PROTECTED]> wrote: > I've attached the message from Ben Kirk. Also > attached is the example > program that he sent out. See below for his original > mail. > > On a side note, I have written a working code with > Matrix-free technique to > solve a nonlinear, transient diffusion-reaction > problem. It still needs few > refinements and I will send it here or maybe upload > it somewhere soon for > all those interested. > > -----Original Message----- > From: Benjamin Kirk [mailto:[EMAIL PROTECTED] > Sent: Wednesday, January 23, 2008 9:40 AM > To: Vijay M; [EMAIL PROTECTED] > Subject: Re: [Libmesh-users] Support for Matrix-free > algorithms > > Here is a really, really raw example, the comments > are not clear right now, > but I wanted to keep you informed. This requires > the latest svn branch to > work. > > Unpack it in the ./examples directory and run make. > > Run it as > > $ ./ex19-dbg -snes_view -r 4 > for a successive approximation which will converge > linearly, and > > $ ./ex19-dbg -snes_view -r 4 -snes_mf_operator > for a matrix-free approach in the iterative solver > which will converge > quadratically. > > > Anyway, I do have a question regarding using PETSc > object with LibMesh. I > > have been trying to use Petsc objects Mats, Vecs > and SNES solver with > > Libmesh but the one thing I cant seem figure out > is how to set the > > nonlinear_solver public attribute of say a > NonlinearImplicitSystem object > to > > a PETSc SNES object which I have created and > initialized separately. > Since, > > the SNES object used in the wrapper > PetscNonlinearSolver is private, I > don¹t > > understand how this can be done. > > > > Have I missed something and taken a completely > wrong path on this ? I > would > > very much appreciate any comments that you can > provide to help me out > here. > > The user interface is totally up for discussion > since I am the only one who > as exercised it to date. (I am sure Roy will have > some comments!) It seems > to me the right approach will be to add a method > which gives the user access > to the SNES object? From there the KSP, Mat, Vec, > PC, etc... can be > accessed. This would be similar to the approach > used in the > PetscLinearSolver. > > -Ben > > > -----Original Message----- > From: li pan [mailto:[EMAIL PROTECTED] > Sent: Wednesday, January 30, 2008 3:25 AM > To: [email protected] > Cc: [EMAIL PROTECTED] > Subject: matrix free scheme > > Dear all, > I remember that there was a discussion about matrix > free scheme with libmesh before X'mas. I'd like to > ask > if somebody has got a example code for this. > > thanx > > pan > > > > ____________________________________________________________________________ > ________ > Never miss a thing. Make Yahoo your home page. > http://www.yahoo.com/r/hs > > No virus found in this incoming message. > Checked by AVG Free Edition. > Version: 7.5.516 / Virus Database: 269.19.16/1251 - > Release Date: 1/30/2008 > 9:29 AM > > > No virus found in this outgoing message. > Checked by AVG Free Edition. > Version: 7.5.516 / Virus Database: 269.19.16/1251 - > Release Date: 1/30/2008 > 9:29 AM > > > ____________________________________________________________________________ ________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ ------------------------------------------------------------------------- This SF.net email is sponsored by: Microsoft Defy all challenges. Microsoft(R) Visual Studio 2008. http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.19.17/1253 - Release Date: 1/31/2008 9:09 AM No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.5.516 / Virus Database: 269.19.17/1253 - Release Date: 1/31/2008 9:09 AM ------------------------------------------------------------------------- This SF.net email is sponsored by: Microsoft Defy all challenges. Microsoft(R) Visual Studio 2008. http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
