During the past forty years computers have dramatically changed engineering, medicine, and science. It is now possible to test thousands of designs and run thousands of trials without first building a prototype for each product or conducting an elaborate experiment for each trial. The impact of this new ability, this power to simulate the real thing, is easy to imagine. Reliability, flexibility, efficiency, and often attractive cost have placed scientific computation as the keystone between theory and applications.
Research in scientific computing uses concepts and methodologies from numerical linear and nonlinear algebra and boundary value problems for differential equations. In addressing these areas scientific computing at Yale emphasizes algorithm development, theoretical analysis, systems modeling, and programming considerations. Algorithm development is concerned with finding new, fast, and/or parallel methods. Theoretical analysis evaluates such questions as rates of convergence, stability, optimality, and operation counts. Systems modeling examines the performance implications of the interactions between computationally intensive algorithms, operating systems, and multiprocessor machines. Programming considerations include coding efficiency, numerical accuracy, generality of application, data structures, and machine independence.
Faculty working in this area are Stanley Eisenstat, Vladimir Rokhlin, and Martin Schultz. Rob Bjornson, Craig Douglas, and Diana Resasco are research scientists.