mathematics

Trilinos

Trilinos is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Trilinos rather than just read about it. In short: Trilinos is a collection of open-source software libraries, called packages, intended to be used as building blocks for the development of scientific applications. The word "Trilinos" is Greek and conveys the idea of "a string of pearls", suggesting a number of software packages linked together by a common infrastructure.

Key takeaways

Trilinos belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Trilinos to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Trilinos from memory before moving on to harder problems.

Reference excerpt

Trilinos is a collection of open-source software libraries, called packages, intended to be used as building blocks for the development of scientific applications. The word "Trilinos" is Greek and conveys the idea of "a string of pearls", suggesting a number of software packages linked together by a common infrastructure. Trilinos was developed at Sandia National Laboratories from a core group of existing algorithms and utilizes the functionality of software interfaces such as BLAS, LAPACK, and MPI. In 2004, Trilinos received an R&D100 Award. Several supercomputing facilities provide an installed version of Trilinos for their users. These include the National Energy Research Scientific Computing Center (NERSC), Blue Waters at the National Center for Supercomputing Applications, and the Titan supercomputer at Oak Ridge National Laboratory.

Features Trilinos contains packages for:

Constructing and using sparse graphs and matrices, and dense matrices and vectors. Iterative and direct solution of linear systems. Parallel multilevel and algebraic preconditioning. Solution of non-linear, eigenvalue and time-dependent problems. PDE-constrained optimization problems. Partitioning and load balancing of distributed data structures. Automatic differentiation Discretizing partial differential equations. Trilinos supports distributed-memory parallel computation through the Message Passing Interface (MPI). In addition, some Trilinos packages have growing support for shared-memory parallel computation. They do so by means of the Kokkos package, which provides a common C++ interface over various parallel programming models, including OpenMP, POSIX Threads, and CUDA.

Programming languages Most Trilinos packages are written in C++. Trilinos version 12.0 and later requires C++11 support. Some Trilinos packages, like ML and Zoltan, are written in C. A few packages, like Epetra, have optional implementations of some computational kernels in Fortran, but Fortran is not required to build these packages. Some Trilinos packages have bindings for other programming languages. These include Python, C, Fortran, and MATLAB.

Software licenses Each Trilinos package may have its own software license. Most packages are Open-source; most of these have a Modified BSD license, while a few packages are under the GNU Lesser General Public License (LGPL). The BLAS and LAPACK libraries are required dependencies.

Worked examples

Example 1 — a first encounter with Trilinos

Start with the simplest possible case. Write down what Trilinos claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Trilinos before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Trilinos ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Trilinos

In research: Trilinos appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Trilinos in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Trilinos is common in secondary-school and first-year university syllabi. It links to neighbouring topics C++ numerical libraries, Concurrent programming libraries, Free mathematics software, so understanding it makes those chapters shorter.
In everyday life: Look for Trilinos outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Trilinos in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Trilinos means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Trilinos out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Trilinos in simple terms?

Why does Trilinos matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Trilinos?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Trilinos.