Title of article :
Accurate radiation boundary conditions for the time-dependent wave equation on unbounded domains
Author/Authors :
Runnong Huan، نويسنده , , Lonny L. Thompson، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2000
Abstract :
Asymptotic and exact local radiation boundary conditions (RBC) for the scalar time-dependent wave equation,
rst derived by Hagstrom and Hariharan, are reformulated as an auxiliary Cauchy problem for each radial
harmonic on a spherical boundary. The reformulation is based on the hierarchy of local boundary operators
used by Bayliss and Turkel which satisfy truncations of an asymptotic expansion for each radial harmonic.
The residuals of the local operators are determined from the solution of parallel systems of linear rst-
order temporal equations. A decomposition into orthogonal transverse modes on the spherical boundary is
used so that the residual functions may be computed e ciently and concurrently without altering the local
character of the nite element equations. Since the auxiliary functions are based on residuals of an asymptotic
expansion, the proposed method has the ability to vary separately the radial and transverse modal orders of the
RBC. With the number of equations in the auxiliary Cauchy problem equal to the transverse mode number,
this reformulation is exact. In this form, the equivalence with the closely related non-re
ecting boundary
condition of Grote and Keller is shown. If fewer equations are used, then the boundary conditions form high-
order accurate asymptotic approximations to the exact condition, with corresponding reduction in work and
memory. Numerical studies are performed to assess the accuracy and convergence properties of the exact and
asymptotic versions of the RBC. The results demonstrate that the asymptotic formulation has dramatically
improved accuracy for time domain simulations compared to standard boundary treatments and improved
e ciency over the exact condition.
Keywords :
Radiation boundary conditions , non-reecting boundary conditions , Wave equation , scattering , unbounded domains , nite ele-ment method
Journal title :
International Journal for Numerical Methods in Engineering
Journal title :
International Journal for Numerical Methods in Engineering