computer science

MFEM

MFEM is a computer science 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 MFEM rather than just read about it. In short: MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license.

MFEM — illustration

Key takeaways

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

Reference excerpt

MFEM is an open-source C++ library for solving partial differential equations using the finite element method, developed and maintained by researchers at the Lawrence Livermore National Laboratory and the MFEM open-source community on GitHub. MFEM is free software released under a BSD license. The library consists of C++ classes that serve as building blocks for developing finite element solvers applicable to problems of fluid dynamics, structural mechanics, electromagnetics, radiative transfer and many other.

Features Some of the features of MFEM include

Arbitrary high order finite elements with curved boundaries. H1, H(curl) and H(div) conforming, discontinuous (L2), and NURBS finite element spaces. Local mesh refinement, both conforming (simplex meshes) and non-conforming (quadrilateral/hexahedral meshes). Highly scalable MPI-based parallelism and GPU acceleration. Wide variety of finite element discretization approaches, including Galerkin, discontinuous Galerkin, mixed, high-order and isogeometric analysis methods. Tight integration with the Hypre parallel linear algebra library. Many built-in solvers and interfaces to external libraries such as PETSc, SuiteSparse, Gmsh, etc. Accurate and flexible visualization with VisIt and ParaView. Lightweight design and conservative use of C++ templating. Documentation in the form of examples and mini-applications.

See also List of computational fluid dynamics software List of finite element software packages List of numerical analysis software List of numerical libraries List of open-source mathematical libraries

References

External links Official website mfem on GitHub Tutorial Publications Seminar

Illustrations

Worked examples

Example 1 — a first encounter with MFEM

Start with the simplest possible case. Write down what MFEM claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, 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 MFEM 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 MFEM 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 MFEM

In research: MFEM appears in computer science 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 MFEM 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: MFEM is common in secondary-school and first-year university syllabi. It links to neighbouring topics C++ numerical libraries, Cross-platform free software, Finite element method, so understanding it makes those chapters shorter.
In everyday life: Look for MFEM 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 MFEM in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what MFEM 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 MFEM out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is MFEM in simple terms?

Why does MFEM matter?

Because it connects several computer science 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 MFEM?

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 MFEM.