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Computational scientists may be employed by universities, government laboratories, or businesses. They often work as part of a team made up of members bringing a variety of different skills. They use the following process in order to solve problems.
- Identify an appropriate real-world phenomenon.
Scientists begin the solution process by defining the problem of interest.
It is important to identify clearly the aspects of the problem that
will be considered. The information that is "known'' about the
problem must be stated. It will be used to ensure that the model represents
the original problem as closely as possible. Then the questions to be
answered must be posed clearly. The scientists may then assemble an
inter-disciplinary team that will most likely include a computer scientist
and a computational scientist. In the landmine-detection1
project, scientists working in diffraction tomography, radar, acoustics,
computer science, and computational science all collaborate.
- Construct a mathematical model.
The mathematical model is usually a very large collection of equations
and inequalities. For example, a mathematical model of a satellite in
earth orbit would include equations of motion, while a mathematical
model used for bridge design would include stress and strain information.
Moving from the original problem to the mathematical model almost always
requires making simplifying assumptions. Perhaps it will be modeled
in 2 dimensions rather than 3, for example. These assumptions will need
to be reconsidered when the results of the numerical experiments are
obtained.
- Design a numerical algorithm.
An algorithm is a set of step-by-step instructions for accomplishing a task.
The algorithm is intended to produce
the solution to a problem or sub-problem by operating on the model.
- Build a computer code that implements the numerical algorithm.
Often, steps in the numerical algorithm are general enough that
they can be implemented in computer code in more than one way. The computational
scientist will need to decide how to implement the algorithm efficiently
on the type of computer that will be used to solve the problem. Many
of the steps in the algorithm may be implemented by using existing software;
others will require new code to be written.
- Perform numerical experimentation (simulation) with the intention
of:
- evaluating (validating) and revising (if necessary) the model.
If the results replicate behavior that scientists know to be valid,
then they will have more confidence that the predictions of the
model will also be of value. Sometimes, results from simulations
will lead to additional questions about the phenomenon being studied,
and the mathematical model will need to be modified to reflect a
new direction of research. Occasionally, researchers will realize
at this point that they forgot to include some piece of information
(for example, that a particular value can never be negative) that
is common sense to a person, but must be stated explicitly in a
mathematical model.
- generating mathematical conjecture and subsequent new theory
concerning numerical and theoretical properties of both the model
and the algorithm.
Computational scientists must develop a background in basic science, mathematics,
and computer science; but the work they do is not the same as the work
of a scientist, mathematician, or computer scientist. How it differs is
explained in the next section.
Note: The following links will open in a new window.
1 Landmine Detection Links
- A
Survey of the Field This work
was done by Magda El-Shenawee as part of her project with the Demining team
led by Carey Rappaport at Northeastern University, Boston.
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