Computing in Science and Engineering

Solutions of the Schrodinger equation that pertain to different energies are orthogonal by virtue of quantum dynamics. However, when we obtain such solutions numerically using library differential equation solvers, and when the inner product is defined by numerical quadrature, the result is not sufficiently orthogonal for certain purposes. This paper shows how to construct stable finite-difference schemes that preserve accurate numerical orthogonality of the solutions.

Correctness is more precious to scientific programmers than it is to business programmers because of the great difficulty in distinguishing between programming errors, errors in modeling, and errors in algorithms. We've all sat in meetings and discussed whether a peculiar wiggle in a graph represents an algorithm problem (such as neglecting to include a possibly negligible term) or a modeling one (such as ignoring a possibly important physical process). Usually it turns out to be nothing so esoteric: we come back the next week and learn that it was a bug.

As educators know, the more a student interacts with a subject, the better he or she will learn it. This is particularly true in technical subjects. One way to promote interaction is to have "laboratories" in which the student manipulates objects on the computer screen using the keyboard or mouse and then sees those actions' outcome.

Over the past decades, the computational science community has debated the best architecture for parallel computing. However, experience has found there is an almost irreconcilable difference between the way users would like to write their software and the way machines must be instructed to run efficiently. The use of message passing in parallel computing is a reasonable decision, because the resultant code probably runs well on all architectures. This choice is not a trivial decision: it requires substantial work over and above that needed in the sequential case.

Model validation is a crucial process that underpins model development and gives confidence to the results from running models. This article discusses a range of techniques for validating atmosphere models given that the atmosphere is chaotic and incompletely observed.

Interactions between the atmosphere, ocean, ice, land surface, and the marine and terrestrial biosphere control the global climate system. These components are coupled by the exchange of momentum, radiative energy, and trace constituents' mass. Various processes drive this exchange and require different computational methods to model it.