About -
Understanding, validating, using and developing algorithms and software tools for distributed linear algebra solvers, like Krylov accelerators and preconditioners, requires input data. This data should have three critical properties:
- reflect real-life applications to a sufficient extent so that we can use them to predict performance;
- be sufficiently simple to be amenable to mathematical analysis;
- it is possible to write generators that easily provide instances of these problems.
As regards real-life applications, we have here selected PDE-type problems.
Although Galeri can generate some non-PDE linear systems, surely there is a
strong focus on PDE applications. Among them, the Laplace problem is probably
the most widely studied application, and a broad range of results are
available. For most solvers and preconditioners, often there is a sharp
convergence bound that can be used to validate a particular class, or to
get a sense of the performances of a new method. A Trilinos package that uses
Galeri is the
MatrixPortal module of
WebTrilinos.
Galeri's Matrix generation capabilities can help to make examples shorter
and easier to read, since they can produce challenging linear systems in a few
code lines. Therefore, the attention of the example's reader is not distracted
by complicated instructions aiming to build this or that linear system. Since
most linear algebra packages of Trilinos use Galeri, users will quickly become
familiar with it.
Galeri is used in the examples of the
Amesos,
IFPACK, and
ML
packages.
Finally, Galeri is very convenient for software testing. A large variety of problems can be produced, to understand or validate the performances of a given class. Galeri is used in the testing of Amesos, IFPACK, and ML.
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