DE Seminar: Ephraim Ruttenberg
UMBC Undergraduate Student
Location
Mathematics/Psychology : 401
Date & Time
October 21, 2024, 11:00 am – Oct 28, 2024 12:00 pm
Description
Title: Inverse
Iteration for the Principal Laplace Eigenvalue and Related Problems in Optimal
Insulation
Speaker: Ephraim Ruttenberg
Abstract: The Laplacian
operator has a discrete, positive spectrum whose smallest
("principal") element is simple, i.e. it has multiplicity 1. This
principal eigenvalue is impossible to compute analytically for most domains,
but it admits a variational characterization in terms of the Rayleigh quotient.
A technique from finite-dimensional linear algebra known as Inverse Iteration
can be used to approximate its value, and the application of this method has
been well-studied in the presence of Dirichlet boundary conditions. We outline
the application of Inverse Iteration to Robin boundary conditions as well as
mixed Neumann-Dirichlet boundary conditions.
We also describe a problem in optimal insulation which we hope to be able to
apply Inverse Iteration to in the future. This work was done over the Summer at
the Lafayette College REU in collaboration with Ben Lyons and Nick Zitzelberger
under the mentorship of professors Farhan Abedin and Jun Kitagawa.
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