Talk (non-conference) (Invited)

FZJ-2021-01532

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png The hot spots conjecture can be false: Some numerical examples using boundary integral equations

Kleefeld, A. (Corresponding author)FZJ*

2021

Please use a persistent id in citations: http://hdl.handle.net/2128/27507

Abstract: The hot spots conjecture is only known to be true for special geometries. It can be shown numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Enabling Computational- & Data-Intensive Science and Engineering (POF4-511) (POF4-511)

Appears in the scientific report 2021

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Database coverage:

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