[petsc-users] newbie questions on preconditioner LU

[Ling Zou]

Hi, All

I am trying to understand how the preconditioner works when using KSP.

For example, when using KSP to solve the linear system problem,

Ax = b

with the default left preconditioning. We actually solve,

M^(-1) * A x = M^(-1) * b

where, M is the preconditioning matrix and in many cases, we just use A as
the preconditioning matrix.


Question:
1), Is the understanding above correct?

2), If the understanding above is correct, is it correct to state the
different methods provided in PETSc (such as PCLU, PCILU, etc) are to
calculate the inverse matrix M^(-1) from M?

3), How to understand this sentence in the manual (PETSc Users Manual,
Reversion 3.3, page 78, under 4.4 Preconditioners)
"The direct preconditioner, PCLU, is, in fact, a direct solver for the
linear system that uses LU factorization. PCLU is included as a
preconditioner so that PETSc has a consistent interface among direct and
iterative linear solvers."
Does this indicate when using PCLU, we solve Ax = b directly using LU
factorization, or, we solve M^(-1) from M using LU factorization?

As a beginner to the PETSc, all questions are probably too simple. I'd
appreciate it if someone could answer my questions.

Best,

Ling
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