Accurate radiation boundary conditions for the time-dependent wave equation on unbounded domains

2000 ◽  
Vol 47 (9) ◽  
pp. 1569-1603 ◽  
Author(s):  
Runnong Huan ◽  
Lonny L. Thompson
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Unbounded Domains ◽  
Time Dependent ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary

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].

Asymptotic and Exact Radiation Boundary Conditions for Time-Dependent Scattering

1999 ◽  
Author(s):  
Lonny L. Thompson ◽  
Runnong Huan
Keyword(s):  
Cauchy Problem ◽  
Finite Element ◽  
Boundary Conditions ◽  
Near Field ◽  
Three Dimensions ◽  
Time Dependent ◽  
Radiation Boundary Condition ◽  
Radiation Boundary Conditions ◽  
First Order ◽  
Radiation Boundary

Abstract Asymptotic and exact local radiation boundary conditions first derived by Hagstrom and Hariharan are reformulated as an auxiliary Cauchy problem for linear first-order systems of ordinary equations on the boundary for each harmonic on a circle or sphere in two- or three-dimensions, respectively. With this reformulation, the resulting radiation boundary condition involves first-order derivatives only and can be computed efficiently and concurrently with standard semi-discrete finite element methods for the near-field solution without changing the banded/sparse structure of the finite element equations. In 3D, with the number of equations in the Cauchy problem equal to the mode number, this reformulation is exact. If fewer equations are used, then the boundary conditions form uniform asymptotic approximations to the exact condition. Furthermore, using this approach, we formulate accurate radiation boundary conditions for the two-dimensional unbounded problem on a circle. Numerical studies of time-dependent radiation and scattering are performed to assess the accuracy and convergence properties of the boundary conditions when implemented in the finite element method. The results demonstrate that the new formulation has dramatically improved accuracy and efficiency for time domain simulations compared to standard boundary treatments.

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