On an Eigenvalue Property of Summation-By-Parts Operators
(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:
https://lup.lub.lu.se/record/65683a46-243f-45c0-a4ed-8c82367bc6c0
- author
- Linders, Viktor LU
- organization
- publishing date
- 2022-12
- 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}}, }