[petsc-users] Problems about Preconditioner in SNES

[Yingjie Wu]

Respected Petsc developers:
Hi,
Recently, I developed a two-dimensional non-linear equations solver (SNES)
using Petsc to solve temperature, velocity and pressure fields.  Since the
coupling characteristics of the problem are complex, it is difficult to
construct Jacobian matrix explicitly, so Matrix-Free method with
Preconditioner is adopted.  I have the following questions about the
Petsc's Preconditioner.

1. Is the preconditioning matrix updated in linear or non-linear steps?
Because the elements in my preconditioning matrix are functions of
variables (such as density is a function of temperature and pressure, and
preconditioning matrix elements often contain density).

2.For some problems the preconditioning matrix element are constant, if it
possible that the preconditioning matrix is constructed and decomposed only
once at the beginning of the program and used for subsequent calculation?

3. What is the difference between using Matrix-Free method and using normal
Newton method for preconditioning matrix?
As far as I know, when using the Matrix-Free method, the type of
preconditioning matrix needs to be defined as MATMFFD. Are there any other
differences?

Thanks,
Yingjie
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