(Description of Seminar 9)
Oct. 28, 1997
On last wednesday, Dr. Jianping Zhu gave us a lecture about Efficient and Accurate Local Time Stepping Algorithms for Multi-rate Problems. Dr. Jianping Zhu is a professor of Department of Mathematics, Mississippi State University.
Dr. Zhu first gave some introduction about the original local stepping algorithm, including explicit method and implicit method. A multi-rate problem was described by a system of coupled partial differential equations with different time scales associated with different equations in the system. The numerical solutions to such a system was calculated using a time step determined by the most restrictive time scale in the system for stability and accuracy considerations.
He demonstrated in this talk that this time step could be excessively small and unnecessary in many situations, and discussed a more efficient time integration method that uses different time steps for different equations depending on their time scales. Numerical results for reaction-diffusion equations with linear diffusion terms and nonlinear reaction terms will be presented to demonstrate significant improvement in computational efficiency.