[Amath-seminars] Boeing Colloquium Thursday, Oct. 27

[Amin Rahman]

Dear All,

Our Boeing Colloquium this week, presented by Professor Sigal Gottlieb of
University of Massachusetts at Dartmouth (
https://www.umassd.edu/cas/math/people/faculty-and-staff/sigal-gottlieb/),
will be held on Thursday, Oct. 27, 2022, 4 – 5 p.m. in Smith Hall 205.

Title: Developing high order, efficient, and stable time-evolution methods
using a time-filtering approach.

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 enables 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.


Best regards,
Amin

-- 
Aminur (Amin) Rahman (He/him/his)
Acting Instructor (postdoc)
Department of Applied Mathematics
http://faculty.washington.edu/arahman2
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