1.1 What is Computational Science?

With computers, scientists and engineers have made numerous discoveries that they would not have made otherwise. In fact, computers have revolutionized the way that many scientists do their work.

Solve 2x + 5 = 7. Sure, that's easy enough. Or solve a system of two equations and two unknowns like

You don't need a computer for that. But imagine solving a problem by hand with 3 million variables. That's how many are required in the Spectral Element Ocean Model¹, a vast computer simulation, that tests the wind's effects on the Earth's oceans. Problems of this magnitude, common in today's science, wouldn't be possible without computers.

Traditionally, science was done in a laboratory as a combination of theory and physical experimentation (which included hand calculations), but computers have made possible a new and powerful way of doing science -- numerical simulation -- that augments the old. Numerical simulation is the process of modeling mathematically a physical phenomenon, and then running an experiment with the mathematical model. Computational mathematicians or computational scientists play a major role in this new way of doing science, creating, evaluating, and refining the mathematical models used to simulate the physical phenomena.

Simulation can be used when physical experiments are too costly, time consuming, dangerous, or even impossible. Since it is infeasible to physically experiment with landmine detection devices, scientists are experimenting with a computer model. At the center of a $5-million Army Research Office initiative to develop new technologies for detecting landmines is a complicated, three-dimensional computer model of dirt.² Running simulations with the dirt model will show researchers the best way to set up a system to sense the landmines.

Caption: Output of the landmine simulations. The left image shows the column of dirt without a buried mine. The center image shows the similar signature of a column of dirt that does contain a mine. And the final image shows the mine exposed after the data from the first image has been subtracted from the data in the second. Image: Courtesy of NCSA

Other experiments occur over a time scale that makes physical experiments impossible. For example, over 40 years of data is fed into the Spectral Element Ocean Model.

The availability of high speed networks allows scientists to collaborate with colleagues in other locations and run their experiments on computers located in other places. In the Spectral Element Ocean Model, biologists work with oceanographers to develop biological models from the ocean model. Fishery scientists use it to see if the yearly fluctuations of salmon populations along the Alaskan coastline could be related to atmospheric and oceanic conditions. Knowing this could help determine how much salmon should be fished in a year to maximize the salmon population.

Computational science is an interdisciplinary field at the intersection of three domains: mathematics, computer science, and the biological and physical sciences. The computational scientist uses tools from computer science and mathematics to study problems from physical science, social science, engineering, etc.

Most of the problems that computational scientists work on involve vast amounts of data and a large number of variables. Through the advances in computer technology and numerical methods, mathematicians and scientists are able to work together modeling and solving problems that were impossible to address ten years ago.

Computational scientists do more than use a computer to find solutions to mathematical models developed from scientific problems however. They also develop new mathematical tools and theory and develop new numerical methods and improve the accuracy and speed of existing methods.

The next section gives a brief overview of how this happens.

Note: The following links will open in a new window.