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Variational Principles and Conservation Laws in the Derivation of Radiation Boundary Conditions for Wave Equations
Edwin F. G. Van Daalen, Jan Broeze and Embrecht Van Groesen
Mathematics of Computation
Vol. 58, No. 197 (Jan., 1992), pp. 55-71
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2153020
Page Count: 17
You can always find the topics here!Topics: Boundary conditions, Wave equations, Flux density, Velocity, Lagrangian function, Mathematics, Conservation laws, Klein Gordon equation, Euler Lagrange equation, Momentum
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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.
Mathematics of Computation © 1992 American Mathematical Society