TY - JOUR
T1 - Variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations
AU - van Daalen, Edwin F.G.
AU - Broeze, Jan
AU - van Groesen, Embrecht
PY - 1992
Y1 - 1992
N2 - Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some appropriate density—such as the energy density—as well as possible. The theory is applied to a nonlinear version of the Klein-Gordon equation. For this application numerical test results are presented. In an accompanying paper the theory is applied to a two-dimensional wave equation.
AB - Radiation boundary conditions are derived for partial differential equations which describe wave phenomena. Assuming the evolution of the system to be governed by a Lagrangian variational principle, boundary conditions are obtained with Noether's theorem from the requirement that they transmit some appropriate density—such as the energy density—as well as possible. The theory is applied to a nonlinear version of the Klein-Gordon equation. For this application numerical test results are presented. In an accompanying paper the theory is applied to a two-dimensional wave equation.
UR - http://www.scopus.com/inward/record.url?scp=84968466811&partnerID=8YFLogxK
U2 - 10.1090/S0025-5718-1992-1106985-6
DO - 10.1090/S0025-5718-1992-1106985-6
M3 - Article
SN - 0025-5718
VL - 58
SP - 55
EP - 71
JO - Mathematics of computation
JF - Mathematics of computation
IS - 197
ER -