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On an Eigenvalue Property of Summation-By-Parts Operators

Linders, Viktor LU (2022) In Journal of Scientific Computing 93(3).
Abstract

Summation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and accuracy rely on the assumption that the SBP operator possesses a particular eigenvalue property. In this note, three results pertaining to this property are proven. Firstly, the eigenvalue property does not hold for all nullspace consistent SBP operators. Secondly, this issue can be addressed without affecting the accuracy of the method by adding a specially designed, arbitrarily small perturbation term to the SBP operator. Thirdly, all pseudospectral methods satisfy the eigenvalue property.

Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Eigenvalues, Nullspace consistency, Pseudospectral methods, Summation-By-Parts
in
Journal of Scientific Computing
volume
93
issue
3
article number
82
publisher
Springer
external identifiers
  • scopus:85141635984
ISSN
0885-7474
DOI
10.1007/s10915-022-02042-z
language
English
LU publication?
yes
id
65683a46-243f-45c0-a4ed-8c82367bc6c0
date added to LUP
2022-12-05 11:04:24
date last changed
2022-12-05 11:04:24
@article{65683a46-243f-45c0-a4ed-8c82367bc6c0,
  abstract     = {{<p>Summation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and accuracy rely on the assumption that the SBP operator possesses a particular eigenvalue property. In this note, three results pertaining to this property are proven. Firstly, the eigenvalue property does not hold for all nullspace consistent SBP operators. Secondly, this issue can be addressed without affecting the accuracy of the method by adding a specially designed, arbitrarily small perturbation term to the SBP operator. Thirdly, all pseudospectral methods satisfy the eigenvalue property.</p>}},
  author       = {{Linders, Viktor}},
  issn         = {{0885-7474}},
  keywords     = {{Eigenvalues; Nullspace consistency; Pseudospectral methods; Summation-By-Parts}},
  language     = {{eng}},
  number       = {{3}},
  publisher    = {{Springer}},
  series       = {{Journal of Scientific Computing}},
  title        = {{On an Eigenvalue Property of Summation-By-Parts Operators}},
  url          = {{http://dx.doi.org/10.1007/s10915-022-02042-z}},
  doi          = {{10.1007/s10915-022-02042-z}},
  volume       = {{93}},
  year         = {{2022}},
}