Variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations

van Daalen, Edwin F. G.; Broeze, Jan; van Groesen, Embrecht

doi:10.1090/S0025-5718-1992-1106985-6

Variational principles and conservation laws in the derivation of radiation boundary conditions for wave equations
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by Edwin F. G. van Daalen, Jan Broeze and Embrecht van Groesen PDF

Math. Comp. 58 (1992), 55-71 Request permission

Abstract:

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.

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