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Time-Accurate and highly-Stable Explicit (TASE) operators for stiff differential equations

Event Type: 
Date and Time: 
Friday, January 10, 2020 - 16:30
Location: 
CTR Conference Room 103
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Speaker(s): 
Dr. Maxime Bassenne

Unconditionally stable implicit time-marching methods are powerful in efficiently solving stiff differential equations. In this talk, I will present a novel unified framework for handling both physical and numerical stiffness based on Time-Accurate and highly-Stable Explicit (TASE) operators.

The proposed TASE operators act as preconditioners on the stiff terms and can be readily deployed to most existing explicit time-marching methods. The resulting time integration method remains the original explicit time-marching schemes, yet with nearly unconditional stability. The TASE operators can be designed to be arbitrarily high-order accurate such that the original explicit time-marching accuracy order is preserved. I will illustrate the performance of the TASE method on a set of benchmark problems with strong stiffness. Numerical results demonstrate that the proposed framework preserves the high-order accuracy of the explicit time-marching methods with very-large time steps for all the considered cases.

Bio: 
Dr. Maxime Bassenne is a postdoctoral research fellow in the Laboratory of Artificial Intelligence in Medicine and Biomedical Physics in the Stanford Radiation Oncology department. He received his PhD degree in Mechanical Engineering from Stanford University in 2019. His research interests broadly revolve around advancing computational science to solve problems in engineering and medicine.