Complete Radiation Boundary Conditions for Maxwell’s Equations


  • Thomas Hagstrom Department of Mathematics Southern Methodist University Dallas TX, USA
  • John Lagrone Department of Mathematics Tulane University New Orleans LA, USA


radiation boundary conditions, time-domain methods


We describe the construction, analysis, and implementation of arbitrary-order local radiation boundary condition sequences for Maxwell’s equations. In particular we use the complete radiation boundary conditions which implicitly apply uniformly accurate exponentially convergent rational approximants to the exact radiation boundary conditions. Numerical experiments for waveguide and free space problems using high- order discontinuous Galerkin spatial discretizations are presented.


T. Hagstrom and T. Warburton, “Complete radiation boundary conditions: minimizing the long time error growth of local methods,” SIAM J. Numer. Anal., vol. 47, pp. 3678–3704, 2009.

W. Chew and W. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microwave Optical Technol. Lett., vol. 7, pp. 599–604, 1994.

J. Hesthaven and T.Warburton, “High-order/spectral methods on unstructured grids. I. Time-domain solution of Maxwell’s equations,” J. Comput. Phys., vol. 181, pp. 186–221, 2002.

T. Hagstrom, “High-order radiation boundary conditions for stratified media and curvilinear coordinates,” J. Comput. Acoust., vol. 20, 2012.

——, “Extension of complete radiation boundary conditions to dispersive waves,” in Waves 2017, 2017, pp. 175–176.

T. Hagstrom and S. Lau, “Radiation boundary conditions for Maxwell’s equations: A review of accurate time-domain formulations,” J. Comput. Math., vol. 25, pp. 305–336, 2007.

B. Alpert, L. Greengard, and T. Hagstrom, “Rapid evaluation of nonreflecting boundary kernels for time-domain wave propagation,” SIAM J. Numer. Anal., vol. 37, pp. 1138–1164, 2000.

——, “Nonreflecting boundary conditions for the time-dependent wave equation,” J. Comput. Phys., vol. 180, pp. 270–296, 2002.

T. Hagstrom, D. Givoli, D. Rabinovich, and J. Bielak, “The double absorbing boundary method,” J. Comput. Phys., vol. 259, pp. 220–241, 2014.

J. Lagrone and T. Hagstrom, “Double absorbing boundaries for finitedifference time-domain electromagnetics,” J. Comput. Phys., vol. 326, pp. 650–665, 2016.

K. Juhnke, “High-order implementations of the double absorbing boundary,” Ph.D. dissertation, Southern Methodist University, 2017