Dear libMesh developers and users,
I want to use matrix-free method and am looking into ShellMatrix in libMesh. To
get started, I've looked at the ShellMatrix example in example 4 under
Miscellaneous folder, and got several questions:
1. In the example of ShellMatrix, why building the system stiffness matrix? If
we use ShellMatrix, is there a need to explicitly build the system stiffness
matrix? My understanding is, the system stiffness matrix in this example is
used to demonstrate the SumShellMatrix, is it correct?
2. If I use only TensorShellMatrix, without SumShellMatrix, I still need to
build RHS in the assemble function and attach it to the EquationSystem, is it
correct?
3. In order to build any user-defined mac-vec multiplication, I think we
can create our own userShellMatrix.h and userShellMatrix.C, and define
user-specific vector_mult(), vector_mult_add(), get_diagonal(), m() and
n(), just as TensorShellMatrix and SumShellMatrix did. After this, we
recompile libmesh, then we can start using userShellMatrix, and we don't
need to worry about implementing solving the linear system using
MatShell in PETSc since it's already coded up in libMesh solver, is it
correct?
4. The general procedure to use ShellMatrix in my mind is the following: (take
userShellMatrix for example)
system.attach_assemble_function (assemble); // to build RHS
userShellMatrix<Number> shellMatrix(...); // define mat-vec
multiplication
system.attach_shell_matrix(&shellMatrix);
system.solve();
system.detach_shell_matrix();
Is it correct?
Regards, and thanks in advance for any answers.
Xikai Jiang
Postdoctoral Researcher
Materials Science Division, Argonne National Laboratory
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