>> Can you write me the exact expression of the problem you're solving?
The example I forwarded you earlier by Benjamin Kirk solves the
LaplaceYoung problem. I have linked a paper by C.F. Scott et al on
"Computation of capillary surfaces for the LaplaceYoung 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 =3D (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=20
J*delu =3D residual =3D 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: libmeshusersbounces@...
[mailto:libmeshusersbounces@...] On Behalf Of li pan
Sent: Thursday, January 31, 2008 8:05 AM
To: Vijay S. Mahadevan
Cc: libmeshusers@...
Subject: Re: [Libmeshusers] 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
(Jacobianfree Newton=96Krylov 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=20
J*r_0 =3D (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" <vijay.m@...> 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.
>=20
> On a side note, I have written a working code with
> Matrixfree technique to
> solve a nonlinear, transient diffusionreaction
> problem. It still needs few
> refinements and I will send it here or maybe upload
> it somewhere soon for
> all those interested.
>=20
> Original Message
> From: Benjamin Kirk [mailto:benjamin.kirk@...]=20
> Sent: Wednesday, January 23, 2008 9:40 AM
> To: Vijay M; libmeshdevel@...
> Subject: Re: [Libmeshusers] Support for Matrixfree
> algorithms
>=20
> 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.
>=20
> Unpack it in the ./examples directory and run make.
>=20
> Run it as
>=20
> $ ./ex19dbg snes_view r 4
> for a successive approximation which will converge
> linearly, and
>=20
> $ ./ex19dbg snes_view r 4 snes_mf_operator
> for a matrixfree approach in the iterative solver
> which will converge
> quadratically.
>=20
> > 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
> don=B9t
> > understand how this can be done.
> >=20
> > 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.
>=20
> 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.
>=20
> Ben
>=20
>=20
> Original Message
> From: li pan [mailto:li76pan@...]=20
> Sent: Wednesday, January 30, 2008 3:25 AM
> To: libmeshusers@...
> Cc: vijay.m@...
> Subject: matrix free scheme
>=20
> 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.
>=20
> thanx
>=20
> pan
>=20
>=20
> =20
>
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