[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Numerical Analysis

arXiv:2402.00846 (math)
[Submitted on 1 Feb 2024]

Title:Computing scattering resonances of rough obstacles

Authors:Frank Rösler, Alexei Stepanenko
View PDF
Abstract:This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric assumptions on the obstacle there exists an algorithm whose output is guaranteed to converge to the set of resonances of the problem. The result is formulated using the framework of Solvability Complexity Indices. The proof is constructive and provides an efficient numerical method. The algorithm is based on a combination of a Glazman decomposition, a polygonal approximation of the obstacle and a finite element method. Our result applies in particular to obstacles with fractal boundary, such as the Koch Snowflake and certain filled Julia sets. Finally, we provide numerical experiments in MATLAB for a range of interesting obstacle domains.
Comments: 35 pages, 13 figures
Subjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP); Spectral Theory (math.SP)
MSC classes: 81U24, 47N40, 65N15
Cite as: arXiv:2402.00846 [math.NA]
  (or arXiv:2402.00846v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2402.00846

Submission history

From: Alexei Stepanenko [view email]
[v1] Thu, 1 Feb 2024 18:38:10 UTC (9,484 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.NA
< prev   |   next >
new | recent | 2024-02
Change to browse by:
cs
cs.NA
math
math.AP
math.SP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)