Dr. David Ketcheson from KAUST will be speaking on March 13th at 4:00 p.m in 135 TMCB.
Title: Better time discretizations for PDEs
Many important phenomena are modelled by time-dependent partial differential equations whose accurate solution is challenging and costly. Numerical algorithms for these problems must satisfy particular stability and accuracy constraints while marching as rapidly as possible. I will introduce some examples of valuable but costly time-dependent wave equation computations. Then I will give an introduction to key stability concepts in time discretization of PDEs, followed by a description of my recent work aimed at answering questions like
- How can we design accurate, stable numerical methods that march faster in time?
- Can we find methods that ensure positivity of solutions?
- What are the theoretical limits on achievable efficiency of time discretizations for PDEs?