Teaching Numerical Methods for Partial Differential Equations

Lou Rossi, Section Editor of SIAM Review gives an overview of the Education paper in the latest issue:

Most instructors manage two opposing currents in classroom dynamics. The first is a desire to describe the subject in its broadest sense including all the subtleties and nuances. It gives the students a road map to the field, and if they can appreciate it at the time, it provides structure to a course that might otherwise appear to be a loosely connected series of topics. The second is the desire to ground the subject with concrete examples that students can grasp at the finest level.  The examples link prerequisite knowledge with one of the new subjects and provide students with a foundation upon which to construct a deeper understanding. Few courses draw together so many disparate topics as numerical methods for partial differential equations (PDEs).  When first exposed to finite differences for numerical PDEs, students will readily notice the regular structures in matrices, but few texts address these structures systematically and connect them directly to the analytical properties of the solution. There are many good examples, but it’s hard to see the broader landscape. In this Education section article, “Functions of Difference Matrices Are Toeplitz Plus Hankel,” authors Gil Strang and Shev MacNamara fill in some of the big picture by presenting some new results and observations about the structure of difference matrices for approximating solutions to PDEs. (more…)

Q&A with Tim Kelley, SIAM Review Editor-in-Chief

Q&A with Tim Kelley, SIAM Review Editor-in-Chief

SIAM Publications Manager Mitch Chernoff interviews Tim Kelley, SIAM Review Editor-in-Chief:

SIREV is SIAM’s flagship journal, dating from 1959. The current format dates to a widely embraced redesign first seen in 1999’s Volume 41.  Where does SIREV go from here?

SIREV’s challenge is to keep pace with the community. We review the editorial board each year for coverage and diversity. The journal experiments all the time. The Research Spotlights section is an example of that experimentation. I have high expectations for Research Spotlights.

I’m also very pleased with the progress the Education section has made since 1999. Education has published some very significant reports on issues such as CSE program development. I hope that those of us in academia can use these reports to convince our management about the importance of applied and computational mathematics in the curriculum. (more…)

The Mathematics and History of the Trapezoidal Rule

Desmond Higham, Section Editor of SIAM Review, recaps the Survey and Review paper in the September 2014 issue of  SIREV: 

The Survey and Review article in the September issue is “The Exponentially Convergent Trapezoidal Rule,” by Nick Trefethen and André Weideman. It deals with a fundamental and classical issue in numerical analysis—approximating an integral. By focusing on one deceptively simple method, the authors are able to combine a lively, historical overview with an insightful, up-to-date coverage of recent results. We learn about the work of Euler, Gauss, Maclaurin, and Poisson, and some of the 20th century pioneers of numerical analysis. We also learn about high-precision computation, treatment of singularities, choice of contours to integrate along, Gauss and Clenshaw–Curtis quadrature,  Padé approximation, and a “quadrature formula that doesn’t even integrate constants right” (see footnote number 15 in paper).

The first half of the article looks at the mathematics behind the well-known geometric convergence of the trapezoidal rule. Here the two fundamental routes to a proof are (a) exploiting Taylor series and aliasing, and (b) introducing a function that has simple poles at the summation points in order to apply residue calculus. The second half deals with applications where the trapezoidal rule has proved useful, including contour integration, rational approximation, problems with endpoint singularities, inverse Laplace transforms, integral equations, zero finding, special functions, and the numerical solution of parabolic PDEs. (more…)

OSTP Research Priorities

OSTP Research Priorities

SIAM Executive Director Jim Crowley writes: 

The Office of Science and Technology Policy (OSTP) is the agency headed by the U.S. President’s science advisor. Among its duties is to lead interagency efforts to develop and implement sound science and technology policies and budgets. One way it does this is by issuing budget guidance to science agencies as they form their budgets, offering a set of Administration priorities for those agencies.

The 18 July 2014 budget memorandum from current director John Holdren contained seven R&D priorities – one of special note to the SIAM community. The seven were:

  1. Advanced manufacturing and industries of the future.
  2. Clean energy.
  3. Earth observations.
  4. Global climate change.
  5. Information technology and high-performance computing.
  6. Innovation in life sciences, biology, and neuroscience.
  7. National and homeland security.

While the SIAM community can contribute to nearly all of these – the item on national and homeland security specifically mentions hypersonics, for example – it is the item on IT and HPC that most directly relates to the research of many SIAM members. (more…)

Putting a Value on Expository Writing

SIAM Executive Director Jim Crowley writes: 

Why don’t applied mathematicians write more expository articles? How can SIAM promote good expository writing and encourage more members of the community to write such articles?

Part of the reason, of course, is that technical articles, written for experts and published in scholarly journals, are the gold standard for professional applied mathematicians. We write for the few people who work in our own research areas, or perhaps for scientists in the main application areas for our work. But we tend not to spend a lot of time writing for a more general audience – even if that audience is only as broad as the SIAM membership.

Even review articles, written for a large audience, are not the norm in our field. Certainly SIAM Review publishes review articles, but such articles seem to be more highly regarded (and hence rewarded) in other disciplines. You need only look at the list of titles in Annual Reviews to get the sense that perhaps mathematicians do not place such a high value on writing such reviews; or else one would expect an AR to have a publication in mathematics. (more…)

The Optimal Power Flow Problem

The Optimal Power Flow Problem

Stephen Wright, Section Editor of SIAM Review, gives an overview of the Research Spotlights paper in the September 2014 issue of  SIREV: 

The power grid has long been a rich source of problems in mathematical modeling, linear and nonlinear equations, and optimization. An important instance is the optimal power flow problem, which reveals the optimal output of a collection of generators that meets a given set of demands for power around the grid, while respecting limits on current flows along transmission lines. This problem is solved repeatedly on a typical day to take account of fluctuating demands and operating conditions. Operation of the grid has become more complex with the advent of renewable power sources, especially wind farms. The output of these sources is notoriously unpredictable, and if fluctuations are not accounted for during generation planning, excess current on some transmission lines may cause overheating, “tripping” of the lines, and possibly cascading failures, resulting in widespread blackouts. (more…)

Letters from the Editor

Des Higham (University of Strathclyde) writes:

This short blog is essentially an annotated list of generic phrases that academic journal editors might wish to re-hash for use in their decision letters.  I hope this resource will benefit three overlapping groups: those of us who serve as editors, those of us who act as referees and those of us who submit articles. It is built on my experiences as an editor, section editor, reviewer and author. These experiences have generally been positive, but over the years I have become aware that a lack of clarity in the communication process can be a key source of inefficiency and frustration. In writing this blog entry, I realise that (a) some issues that I touch on are already covered to some degree by “template” letters supplied by journals, and (b) every set of referee reports is different. However, I believe that a few general topics are worth mulling over.  (more…)

Optimizing Healthcare

Optimizing Healthcare

At the SIAM Conference on Optimization last month, Dr. Retsef Levi, J. Spencer Standish Professor of Management and professor of operations management at the Sloan School of Management at MIT, gave an invited lecture on “Optimizing and Coordinating Healthcare Networks and Markets.”

Recently, he sat down with SIAM for a Google Hangout interview to talk in detail about the use of optimization models in healthcare management.

Speaking about the importance of design and performance analysis of models arising in the context of health networks, Dr. Levi addressed the challenges faced by researchers in incorporating the complex dynamics of healthcare networks into optimization models.

Levi outlined important decisions that healthcare organizations have to make in order to best use their resources to deliver high quality outcomes to patients, as well as in making priorities under circumstances where resources can be scarce. (more…)

SIAM-UKIE New Media to Help Increase Impact of Members’ Activities in the Wider Community

SIAM-UKIE New Media to Help Increase Impact of Members' Activities in the Wider Community

Endre Süli (University of Oxford), Françoise Tisseur (University of Manchester), and Angela Mihai (Cardiff University) write:

From April 2014, the United Kingdom and Republic of Ireland Section of SIAM (SIAM-UKIE: http://www.siam.org/sections/siamukie/) maintains a bimonthly newsletter which is designed to promote contact and to further facilitate the dissemination of information between the Section’s members from different areas. With an increasing number of SIAM Student Chapters in the UK, and a demand for more frequent updates on their activities, the SIAM-UKIE newsletter was a timely development in the provision of local support for the SIAM members at sectional level. The April and June 2014 issues of the newsletter are free to access via the Section’s News & Events webpage http://blogs.cardiff.ac.uk/siamukie/news-events/ and can also be downloaded from the archive webpage http://www.siam.org/sections/siamukie/archive.php. (more…)

Register Now for the SIAM Conference on Nonlinear Waves and Coherent Structures

Register Now for the SIAM Conference on Nonlinear Waves and Coherent Structures

Richard O. Moore (New Jersey Institute of Technology) writes:

As many of us wrap up the spring semester, our thoughts turn to finalizing summer plans. This summer features the biennial SIAM Conference on Nonlinear Waves and Coherent Structures (NW14), being held at the University of Cambridge in the UK from August 11 to 14. The program has recently been posted, making this an opportune time to point out some highlights of NW14.

What immediately jumps out about NW14 is its sheer size. The number of minisymposia has doubled from 48 at NW12 to 94 in 2014! The number of contributed sessions has seen comparable growth, and the number of plenary talks has grown from five to eight. Only the size of the poster session has decreased, shrinking to 19 from 45 in 2012. Nevertheless, we expect to see a considerably larger attendance this year, well over 400 attendees. (more…)