mathematics

Phillip Colella

Phillip Colella 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 Phillip Colella rather than just read about it. In short: Phillip Colella is an American applied mathematician and a member of the Applied Numerical Algorithms Group at the Lawrence Berkeley National Laboratory. He has also worked at Lawrence Livermore National Laboratory.

Key takeaways

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

Reference excerpt

Phillip Colella is an American applied mathematician and a member of the Applied Numerical Algorithms Group at the Lawrence Berkeley National Laboratory. He has also worked at Lawrence Livermore National Laboratory. He is known for his fundamental contributions in the development of mathematical methods and numerical tools used to solve partial differential equations, including high-resolution and adaptive mesh refinement schemes. Colella is a member of the US National Academy of Sciences.

Career Colella received his bachelor's degree in 1974, Master's degree in 1976, and Ph.D. in 1979 degree from the University of California, Berkeley, all in applied mathematics. He received the Ph.D. degree under the supervision of Alexandre Chorin. He began his research career at Lawrence Berkeley National Laboratory, University of California, California. His primary area of research involves the development of high-resolution schemes and adaptive mesh refinement methods for the solution of partial differential equations. He has also applied computational methods in a variety of scientific and engineering fields, including low-speed incompressible flows, shock wave theory, combustion, magnetohydrodynamics, and astrophysical flows. Colella has also been the leader of a project in NASA's Computational Technologies for Earth and Space Sciences, called "Block-Structured Adaptive Mesh Refinement Methods for Multiphase Microgravity Flows and Star Formation".

Awards and honors Colella is a member of the National Academy of Sciences since 2004 and Fellow of Society for Industrial and Applied Mathematics (SIAM). He is the recipient of many honors, including the Sidney Fernbach Award from the IEEE Computer Society in 1998, given each year to one person who has made "an outstanding contribution in the application of high performance computers using innovative approaches." He has also received the SIAM/ACM prize (with John Bell) for computational science and engineering in 2003.

Selected papers Colella, P.; Woodward, P. R. (April 1984). "Piecewise parabolic method (PPM) for gas-dynamical simulations" (PDF). J. Comput. Phys. 54 (1): 174–201. Bibcode:1984JCoPh..54..174C. doi:10.1016/0021-9991(84)90143-8. Archived from the original (PDF) on 2013-10-01. Colella, P.; Woodward, P. R. (1984). "The numerical simulation of two-dimensional fluid flow with strong shocks" (PDF). J. Comput. Phys. 54 (1): 115–173. Bibcode:1984JCoPh..54..115W. doi:10.1016/0021-9991(84)90142-6. Archived from the original (PDF) on 2009-03-06. Berger, M. J.; Colella, P. (1989). "Local adaptive mesh refinement for shock hydrodynamics" (PDF). J. Comput. Phys. 82 (1): 64–84. Bibcode:1989JCoPh..82...64B. doi:10.1016/0021-9991(89)90035-1. Archived from the original (PDF) on 2016-12-23. Bell, J. B.; Colella, P.; Glaz, H. M. (1989). "A second-order projection method for the incompressible Navier-Stokes equations" (PDF). J. Comput. Phys. 85 (2): 257–283. Bibcode:1989JCoPh..85..257B. CiteSeerX 10.1.1.392.8098. doi:10.1016/0021-9991(89)90151-4. Archived from the original (PDF) on 2016-12-27. {{cite journal}}: Cite uses deprecated parameter |citeseerx= (help)

References

External links Phillip Colella at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Phillip Colella

Start with the simplest possible case. Write down what Phillip Colella 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 Phillip Colella 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 Phillip Colella 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 Phillip Colella

In research: Phillip Colella 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 Phillip Colella 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: Phillip Colella is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Phillip Colella 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 Phillip Colella in 20 minutes

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

Frequently asked questions

What is Phillip Colella in simple terms?

Why does Phillip Colella 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 Phillip Colella?

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 Phillip Colella.