Numerical Methods for Partial Equations Seminar

Wednesday, April 29, 2020 at 9:00am to 10:00am

Virtual Event

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Meeting ID: 987 0389 7131
US : +1 646 558 8656 or +1 669 900 6833
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SPEAKER:  Albert Chern  (Technical University of Berlin) 

TITLE:  An Exact Discretization of Reflectionless Boundaries for Wave Equations


This talk concerns a classical problem in computational wave propagations: How does one truncate an infinite domain to a finite size without introducing reflection waves from the artificial boundaries?  The state-of-the-art approach is attaching to those boundaries a perfectly matched layer (PML).  In the continuous theory, PMLs are subject to an analytically continued wave equation that damps all incident waves without creating any interfacial reflection.  However, it is believed that “numerical reflections” are unavoidable after discretization.  In this talk, I will demonstrate a truly reflectionless discrete PML.  The key is to uncover the geometric mechanism hidden in the differential calculus formalism; in discretizing the theory, approximations are the best one can hope for the latter, while the former often admits exact discretization.

BIO: Albert Chern; currently a postdoc in mathematics at Technical University of Berlin, and will start as an assistant professor in computer science at UC San Diego in Fall 2020.  Research area: computational math, discrete differential geometry, fluid dynamics, computer graphics.

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