Research / Research AreasScientific Computing
As mathematical models become increasingly more detailed and complex, the equations to be solved rapidly exceed our ability to solve them analytically. When this happens, numerical solutions become a useful tool to get a picture of how a system behaves. Then again, as the models become more complex, the size and speed of the computing resources can often become a factor, and designing efficient and accurate numerical solutions can mean the difference between solving and not solving an important problem.
Topics in scientific computing are at the interface between mathematics and computer science. A specialist in scientific computing must wear multiple hats, as he or she must not only understand the equations to be solved, but also the application being modeled. He or she must be able to write computer code on various computer architectures from simple implementations on a single computer to large computer systems involving hundreds or thousands of cores.
Research in scientific computing involves both the creation of new algorithms for emerging mathematical models, and also the redesigning of existing algorithms for emerging computer architectures.
Moving interfaces appear in many applications from immiscible gas/liquid or liquid/liquid flows, to combustion, to bacterial colonies, and so on. Specialized methods such as level set methods and boundary integral methods are examples of advanced numerical methods for scientific computing that are used to solve the challenging model equations that arise in these systems.
Research on moving interface methods improve their accuracy and expand the range of problems that can be solved by these techniques.
Randomness is inherent in any physical system, and in some cases can play a large part in determining activity. Stochastic simulation methods are special techniques designed to quantify behavior in the presence of noise. Such methods combine techniques for quantifying both deterministic and statistical errors.
One particular class of methods are designed to solve stochastic differential equations, which are employed to model situations as diverse as fluctuating stock prices, motion in the presence of thermal fluctuations, and how propagating pulses are affected by quantum noise.