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On stability and conservation properties of (S)epirk integrators in the context of discretized pdes

Birken, Philipp LU ; Meister, Andreas ; Ortleb, Sigrun and Straub, Veronika (2018) 16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016 237. p.617-629
Abstract

Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called ϕ-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a... (More)

Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called ϕ-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a conservation property of the EPIRK schemes is proven.

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Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
A-stability, CFL condition, Conservation, Exponential integrators
host publication
Theory, Numerics and Applications of Hyperbolic Problems II
volume
237
pages
13 pages
publisher
Springer
conference name
16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016
conference location
Aachen, Germany
conference dates
2016-08-01 - 2016-08-05
external identifiers
  • scopus:85049427920
ISBN
9783319915470
DOI
10.1007/978-3-319-91548-7_46
language
English
LU publication?
yes
id
a14b86af-4df9-445d-932f-7d621ae0a817
date added to LUP
2018-07-26 09:27:28
date last changed
2024-03-01 22:29:29
@inproceedings{a14b86af-4df9-445d-932f-7d621ae0a817,
  abstract     = {{<p>Exponential integrators are becoming increasingly popular for stiff problems of high dimension due to their attractive property of solving the linear part of the system exactly and hence being A-stable. In practice, however, exponential integrators are implemented using approximation techniques to matrix-vector products involving functions of the matrix exponential (the so-called ϕ-functions) to make them efficient and competitive to other state-of-the-art schemes. We will examine linear stability and provide a Courant–Friedrichs–Lewy (CFL) condition of special classes of exponential integrator schemes called EPIRK and sEPIRK and demonstrate their dependence on the parameters of the embedded approximation technique. Furthermore, a conservation property of the EPIRK schemes is proven.</p>}},
  author       = {{Birken, Philipp and Meister, Andreas and Ortleb, Sigrun and Straub, Veronika}},
  booktitle    = {{Theory, Numerics and Applications of Hyperbolic Problems II}},
  isbn         = {{9783319915470}},
  keywords     = {{A-stability; CFL condition; Conservation; Exponential integrators}},
  language     = {{eng}},
  month        = {{01}},
  pages        = {{617--629}},
  publisher    = {{Springer}},
  title        = {{On stability and conservation properties of (S)epirk integrators in the context of discretized pdes}},
  url          = {{http://dx.doi.org/10.1007/978-3-319-91548-7_46}},
  doi          = {{10.1007/978-3-319-91548-7_46}},
  volume       = {{237}},
  year         = {{2018}},
}