Collaborative Research: Construction, Analysis, Implementation and Application of New Efficient Exponential Integrators

University Of California - Merced, Merced CA

Investigators

Abstract

As the scale and complexity of scientific and engineering problems grow, computer simulations become a necessary and integral part of the vast majority of research endeavors. An ability to create a computer model of a process under investigation, whether it comes from physics, economics, biology or some other field, provides not only significant cost savings for a study, but also brings insights inaccessible through experimental procedures alone. The growing complexity with which we describe phenomena of interest requires increasingly more sophisticated computer models. In particular, it is important to be able to simulate many complex processes over very long times, which is a computationally intensive and challenging task. This project is focused on developing new computational methods that allow simulating and studying time evolving phenomena from a wide range of scientific and engineering disciplines over long time intervals of interest. The mathematical and computer tools created during this project will enable researchers to study problems at a scale and complexity not possible with currently available computational tools. This project will advance the state-of-the-art in both the theory and practice of time discretization methods. In the course of the project a complete theoretical framework and high performance implementations of the new generation of exponential time integrators will be developed. The new methods will significantly improve computational efficiency of numerical models in many important areas of science and engineering, and will enable simulations at a scale and complexity that are not currently possible. The research will advance core numerical analysis through the development and study of new classes of exponential propagation iterative (EPI) methods such as split, hybrid, partitioned, and Krylov-based techniques. In addition, specialized efficient schemes will be designed and optimized for a wide range of problems. The theoretical work will be complemented by the creation of a mathematical software package that will provide high quality implementations of the most efficient exponential integrators to the broad scientific community.