Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle

J. Broeze; Jan Broeze; Edwin F.G. van Daalen; E.F.G. van Daalen

doi:10.1090/S0025-5718-1992-1106959-5

Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle

J. Broeze, Jan Broeze, Edwin F.G. van Daalen, E.F.G. van Daalen

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Abstract

A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon.

Original language	Undefined
Pages (from-to)	73-82
Number of pages	10
Journal	Mathematics of computation
Volume	0
Issue number	58
DOIs	https://doi.org/10.1090/S0025-5718-1992-1106959-5
Publication status	Published - 1992

Keywords

Well-posedness
variational principle
wave equations
METIS-140892
IR-74995
Conservation laws
Absorbing boundary conditions
radiation boundary conditions

Access to Document

10.1090/S0025-5718-1992-1106959-5

Broeze92radiation

Cite this

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title = "Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle",

abstract = "A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon.",

keywords = "Well-posedness, variational principle, wave equations, METIS-140892, IR-74995, Conservation laws, Absorbing boundary conditions, radiation boundary conditions",

author = "J. Broeze and Jan Broeze and {van Daalen}, {Edwin F.G.} and {van Daalen}, E.F.G.",

year = "1992",

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T1 - Radiation Boundary Conditions for the Two-Dimensional Wave Equation from a Variational Principle

AU - Broeze, J.

AU - Broeze, Jan

AU - van Daalen, Edwin F.G.

AU - van Daalen, E.F.G.

PY - 1992

Y1 - 1992

N2 - A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon.

AB - A variational principle is used to derive a new radiation boundary condition for the two-dimensional wave equation. This boundary condition is obtained from an expression for the local energy flux velocity on the boundary in normal direction. The wellposedness of the wave equation with this boundary condition is analyzed by investigating the energy of the system. Results obtained with this (nonlinear) boundary condition are compared with those obtained with the (linear) first-order absorbing boundary condition suggested by Higdon.

KW - Well-posedness

KW - variational principle

KW - wave equations

KW - METIS-140892

KW - IR-74995

KW - Conservation laws

KW - Absorbing boundary conditions

KW - radiation boundary conditions

U2 - 10.1090/S0025-5718-1992-1106959-5

DO - 10.1090/S0025-5718-1992-1106959-5

M3 - Article

SN - 0025-5718

VL - 0

SP - 73

EP - 82

JO - Mathematics of computation

JF - Mathematics of computation

IS - 58

ER -