Numerische Mathematik

, Volume 141, Issue 4, pp 917–966 | Cite as

Complete radiation boundary conditions for the Helmholtz equation I: waveguides

  • Thomas Hagstrom
  • Seungil KimEmail author


We consider the use of complete radiation boundary conditions for the solution of the Helmholtz equation in waveguides. A general analysis of well-posedness, convergence, and finite element approximation is given. In addition, methods for the optimization of the boundary condition parameters are considered. The theoretical results are illustrated by some simple numerical experiments.


Helmholtz equation Complete radiation boundary condition Waveguide 

Mathematics Subject Classification

65N12 65N30 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsSouthern Methodist UniversityDallasUSA
  2. 2.Department of Mathematics and Research Institute for Basic SciencesKyung Hee UniversitySeoulKorea

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