# Questions tagged [preconditioning]

For questions regarding design and implementation of preconditioners for solving linear systems.

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### Using algebraic multigrid for preconditioning convection-diffusion operators

I implemented a Navier Stokes based on FEM discretization and PETSc for solving the linear system of equations. To create an efficient solution procedure, I follow the paper "Efficient ...
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### What is the current state of polynomial preconditioners?

I wonder what has happened to polynomial preconditioners. I am interested in them, because they appear to be comparatively elegant from a mathematical perspective, but as far as I have read in surveys ...
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### Efficient preconditioner for Augmented Lagrangian

I want to solve a non-linear problem with non-linear equality constrains and I'm using a augmented Lagrangian with a penalty regularization term that, as well known, spoils the condition number of my ...
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### Taxonomy of ILU preconditioners

I learned that for BiCGStab solver for sparse linear systems it's pretty much always necessary to use a preconditioner. I realized by now that choosing a good one is problem dependent. Surfing the ...
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### How can I precondition a non-linear problem before linearization?

When I think of solving non-linear equations, I generally think of linearizing first, then applying a preconditioner to the linear matrix. The thought occurred to me that it might be possible to ...
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### How does matrix scaling influence linear solvers?

For instance, in MUMPS there is option to scale matrix s.t. all rows/columns have the same norm. This claims to decrease condition number and improve numerical properties of the matrix: ftp://cuter.rl....
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### On Vanilla Preconditioners for solving dense $Ax=b$ iteratively

I am looking for preconditioners which don't assume anything about the matrix or its origins. I basically want to be able to type in the following in MATLAB and have quick solving time: ...
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### Are there any open source inverse-based multilevel ILU implementations?

I am very impressed with the serial performance of multilevel inverse-based ILU preconditioners, particularly for heterogeneous Helmholtz, but I am surprised to not be able to find any open source ...
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### What guidelines should I use when searching for good preconditioning methods for a specific problem?

For the solution of large linear systems $Ax=b$ using iterative methods, it is often of interest to introduce preconditioning, e.g. solve instead $M^{-1}(Ax=b)$, where $M$ is here used for left-...
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### What is the advantage of multigrid over domain decomposition preconditioners, and vice versa?

This is mostly aimed for elliptic PDEs over convex domains, so that I can get a good overview of the two methods.
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### Why is my iterative linear solver not converging?

What can go wrong when using preconditoned Krylov methods from KSP (PETSc's linear solver package) to solve a sparse linear system such as those obtained by discretizing and linearizing partial ...
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### Applicability of combinatorial and support preconditioner

There are several correspondences between matrices and graphs, e.g., each matrix is the adjacancy matrix of a weighted graph. The terms support preconditioner or combinatorial preconditioner refer to ...
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