Computer simulation is one of the most useful tools for understanding the world around us and making technological progress. Physical processes, from the atomic scale up to the astronomical, can be described by mathematical models. By programming these models into a computer, we can simulate reality and so understand it better. Our work is to develop the mathematical and computational tools for solving the most difficult and important problems in engineering, life sciences, finance, climate science, and more.
Proper mathematical models governing physical processes typically require numerical methods to be developed. This is effectively done by approximating an infinite level of detail with a finite one, and replacing infinite computing processes with finite ones. These approximations are suitable to implementations on computers, such that in the end useful results may be produced. Our research concerns how well the numerical method matches the mathematical model, and how it should be adapted in order to be most effective.
Some computational problems, like climate simulations, take long time to solve due to the large number of computational operations and the amount of data to be processed. Other problems, like testing many different random mutations of DNA, take long time since one is computing many times. In both cases it is desirable to speed up the computations. One way of computing faster is to let multiple computers work together. Our research entails finding the best ways to program, such that each computer solves a small part of the problem and communicates with the others whenever needed, in order to finally produce the entire answer.
To be able to compute (correctly and quickly) our students learn about mathematical models, numerical methods, and programming. We use student-activating forms of teaching, where the students get practical experience before the theoretical matter is formally introduced. Our research on education concerns how students learn concepts and practical skills within the subject area, and in what way the education can affect how they relate to the subject.