Mathematics faculty and graduate students are invited to attend the PhD Preliminary Exam of Jerett Cherry.

Advisor:  Dr. Wolfgang Bangerth

Committee:  Dr. Yongcheng Zhou, Dr. Olivier Pinaud, Dr. Bret Windom

Title: A Time Averaged Parallel in Time Integration Scheme for Hyperbolic Partial Differential Equations 

Abstract: Parallel in Time Integration methods (PinT)  are generally iterative predict and correct methods which seek to compute solutions to Partial Differential Equations (PDEs) by parallelizing computation in the time dimension, but they are known to converge poorly for hyperbolic PDEs. This research proposal presents a possible modification for PinT methods applied to hyperbolic regimes. After discussing how PinT methods work, the methods we will use in our research, and highlighting the main reason why they might fail, we observe that specific quantities of interest may be reasonably calculated from PinT solutions. The key is that if we use time averaging coupled with PinT then quantities like the average pressure on a subdomain, or the average forces exerted on an object in the domain, appear to have faster convergence properties than the time-dependent solution we get from vanilla PinT. Since this approach has not been explored yet in the PinT literature, we propose to study the efficacy of a time averaged approach to PinT for this dissertation.