Speaker
Prof. Sigal Gottlieb, Fellow of SIAM and AWM, Chancellor Professor of Mathematics University of Massachusetts, Dartmouth
Title
Mathematics Colloquium
Subtitle
Developing high order, efficient, and stable time-evolution methods using a time-filtering approach
Digital Location
https://msstate.webex.com/msstate/j.php?MTID=m0645b9449599c90872beb7d33f9f1727
Abstract: Time stepping methods are critical to the stability, accuracy, and efficiency of the numerical solution of partial differential equations. In many legacy codes, well-tested low-order time-stepping modules are difficult to change; however, their accuracy and efficiency properties may form a bottleneck. Time filtering has been used to enhance the order of accuracy (as well as other properties) of time-stepping methods in legacy codes. In this talk I will describe our recent work on time filtering methods for the Navier Stokes equations as well as other applications. A rigorous development of such methods requires an understanding of the effect of the modification of inputs and outputs on the accuracy, efficiency, and stability of the time-evolution method. In this talk, we show that time-filtering a given method can be seen as equivalent to generating a new general linear method (GLM). We use this GLM approach to develop an optimization routine that enabled us to find new time-filtering methods with high order and efficient linear stability properties. In addition, understanding the dynamics of the errors allows us to combine the time-filtering GLM methods with the error inhibiting approach to produce a third order A-stable method based on alternating time-filtering of implicit Euler method. I will present our new methods and show their performance when tested on sample problems.
Biosketch: Prof. Gottlieb received her PhD degree in 1998 from Brown University. She joined UMass Dartmouth in 1999 as an Assistant Professor, was promoted to Full Professor in 2008, and is currently Chancellor Professor in the Mathematics Department. Since 2013, she has been the (Founding) Director of the Center for Scientific Computing and Visualization Research at UMass Dartmouth. During 2017 - 2021, she served as Deputy Director of NSF ICERM at Brown University. Among others, she is a SIAM fellow (class of 2019) “for her contribution to strong-stability-preserving time discretizations and other schemes for hyperbolic equations, and for her professional services including those to SIAM and women in mathematics" and is an AWM fellow (class of 2021). In 2022, she was named the UMass Dartmouth’s Acting Vice Chancellor for Research.
For more information, please contact: Dr. Vu Thai Luan (luan@math.msstate.edu).