Constructing non-reflecting boundary conditions using summation-by-parts in time

Hannes Frenander; Jan Nordström

doi:10.1016/j.jcp.2016.11.038

Constructing non-reflecting boundary conditions using summation-by-parts in time

Hannes Frenander, Jan Nordström

Linköping University

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.

Original language	English
Pages (from-to)	38-48
Number of pages	11
Journal	Journal of Computational Physics
Volume	331
DOIs	https://doi.org/10.1016/j.jcp.2016.11.038
Publication status	Published - 15 Feb 2017
Externally published	Yes

Keywords

Accuracy
Finite differences
Non-reflecting boundary conditions
Simultaneous approximation terms
Stability
Summation-by-parts

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2016.11.038

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title = "Constructing non-reflecting boundary conditions using summation-by-parts in time",

abstract = "In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.",

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AU - Frenander, Hannes

AU - Nordström, Jan

PY - 2017/2/15

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N2 - In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.

AB - In this paper we provide a new approach for constructing non-reflecting boundary conditions. The boundary conditions are based on summation-by-parts operators and derived without Laplace transformation in time. We prove that the new non-reflecting boundary conditions yield a well-posed problem and that the corresponding numerical approximation is unconditionally stable. The analysis is demonstrated on a hyperbolic system in two space dimensions, and the theoretical results are confirmed by numerical experiments.

KW - Accuracy

KW - Finite differences

KW - Non-reflecting boundary conditions

KW - Simultaneous approximation terms

KW - Stability

KW - Summation-by-parts

UR - https://www.scopus.com/pages/publications/85000983806

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DO - 10.1016/j.jcp.2016.11.038

M3 - Article

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SP - 38

EP - 48

JO - Journal of Computational Physics

JF - Journal of Computational Physics

ER -

Constructing non-reflecting boundary conditions using summation-by-parts in time

Abstract

Keywords

ASJC Scopus subject areas

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