Complete Radiation Boundary Conditions for Convective Waves

2012 ◽  
Vol 11 (2) ◽  
pp. 610-628 ◽  
Author(s):  
Thomas Hagstrom ◽  
Eliane Bécache ◽  
Dan Givoli ◽  
Kurt Stein
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Boundary Conditions ◽  
Radiation Boundary Condition ◽  
Linearized Euler Equations ◽  
Radiation Boundary Conditions ◽  
Local Radiation ◽  
Optimal Efficiency ◽  
Radiation Boundary ◽  
Scalar Equations

AbstractLocal approximate radiation boundary conditions of optimal efficiency for the convective wave equation and the linearized Euler equations in waveguide geometry are formulated, analyzed, and tested. The results extend and improve for the convective case the general formulation of high-order local radiation boundary condition sequences for anisotropic scalar equations developed in [4].

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.

STRESS–VELOCITY COMPLETE RADIATION BOUNDARY CONDITIONS

2013 ◽  
Vol 21 (03) ◽  
pp. 1350003 ◽  
Author(s):  
DANIEL RABINOVICH ◽  
DAN GIVOLI ◽  
THOMAS HAGSTROM ◽  
JACOBO BIELAK
Keyword(s):  
Boundary Condition ◽  
Elastic Waves ◽  
Two Dimensions ◽  
High Order ◽  
Radiation Boundary Condition ◽  
Absorbing Boundary ◽  
Radiation Boundary Conditions ◽  
Long Time ◽  
Radiation Boundary ◽  
The Stability

A new high-order local Absorbing Boundary Condition (ABC) has been recently proposed for use on an artificial boundary for time-dependent elastic waves in unbounded domains, in two dimensions. It is based on the stress–velocity formulation of the elastodynamics problem, and on the general Complete Radiation Boundary Condition (CRBC) approach, originally devised by Hagstrom and Warburton in 2009. The work presented here is a sequel to previous work that concentrated on the stability of the scheme; this is the first known high-order ABC for elastodynamics which is long-time stable. Stability was established both theoretically and numerically. The present paper focuses on the accuracy of the scheme. In particular, two accuracy-related issues are investigated. First, the reflection coefficients associated with the new CRBC for different types of incident and reflected elastic waves are analyzed. Second, various choices of computational parameters for the CRBC, and their effect on the accuracy, are discussed. These choices include the optimal coefficients proposed by Hagstrom and Warburton for the acoustic case, and a simplified formula for these coefficients. A finite difference discretization is employed in space and time. Numerical examples are used to experiment with the scheme and demonstrate the above-mentioned accuracy issues.

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