Complete Radiation Boundary Conditions for Maxwell's Equations

2020 ◽  
Author(s):  
Thomas Hagstrom ◽  
John Lagrone
Keyword(s):  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary

Complete Radiation Boundary Conditions for Maxwell’s Equations

2021 ◽  
Vol 35 (11) ◽  
pp. 1290-1291
Author(s):  
Thomas Hagstrom ◽  
John Lagrone
Keyword(s):  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Numerical Experiments ◽  
Maxwell's Equations ◽  
Arbitrary Order ◽  
Rational Approximants ◽  
Radiation Boundary Condition ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Radiation Boundary

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.

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

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