A formulation of asymptotic and exact boundary conditions using local operators

Hagstrom, Thomas; Hariharan, S. I.

doi:10.1016/s0168-9274(98)00022-1

Cited by 155 publications

(149 citation statements)

References 6 publications

(7 reference statements)

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“…This is achieved by employing special auxiliary variables. In Hagstrom and Hariharan (1998), the OBCs are implemented using FDs. Huan and Thompson (2000;2001) implemented the same OBCs with FEs in 3D and 2D, respectively.…”

Section: Extension Of the Hagstrom -Hariharan Conditions To Dispersivmentioning

confidence: 99%

“…First, we recall the essential facts from Hagstrom and Hariharan (1998). The standard wave equation in either the 2D-cylindrical or 3D-spherical case is:…”

Section: Extension Of the Hagstrom -Hariharan Conditions To Dispersivmentioning

confidence: 99%

“…Some highly-accurate OBCs have been proposed for specific classes of nonlinear wave problems (Tsynkov, 1998;Givoli, 1999b;Hagstrom, 1999). This paper describes extension to previous works by Higdon (1994) and Hagstrom et al (1998) with the goal of solving the linear time-dependent wave problem in a dispersive media. The Higdon OBC is a family of OBCs useful for analyzing dispersive wave problems on Cartesian coordinates, but whose implementation was considered impractical beyond the third order.…”

Section: Introductionmentioning

confidence: 96%

“…the Bayliss -Turkel conditions [Bayliss and Turkel, 1980] constitute such a sequence), but before the mid 90s they had been regarded as impractical beyond second or third order from the implementation point of view. Recently, practical highorder local OBCs have been introduced (Collino, 1993;Grote and Keller, 1996;Hagstrom et al, 1998;Guddati and Tassoulas, 2000;Givoli, 2001;Givoli and Patlashenko, 2002) that do not involve high-order derivatives. This is enabled by the introduction of special auxiliary variables on B.…”

Section: Introductionmentioning

confidence: 99%

“…However, some exact and highorder schemes have been devised in this case as well. These include the schemes proposed by Collino (1993), Grote and Keller (1996), Hagstrom et al (1998), Guddati and Tassoulas (2000) and Givoli (2001).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

High-order Non-reflecting Boundary Conditions for Dispersive Waves in Cartesian, Cylindrical and Spherical Coordinate Systems

Joolen

Givoli

Neta

2003

International Journal of Computational Fluid Dynamics

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Dedicated to Professor Mutsuto Kawahara on the occasion of his 60th birthdayAmong the many areas of research that Professor Kawahara has been active in is the subject of open boundaries in which linear time-dependent dispersive waves are considered in an unbounded domain. The infinite domain is truncated via an artificial boundary B on which an open boundary condition (OBC) is imposed. In this paper, Higdon OBCs and Hagstrom -Hariharan (HH) OBCs are considered. Higdontype conditions, originally implemented as low-order OBCs, are made accessible for any desired order via a new scheme. The higher-order Higdon OBC is then reformulated using auxiliary variables and made compatible for use with finite element (FE) methods. Methodologies for selecting Higdon parameters are also proposed. The performances of these schemes are demonstrated in two numerical examples. This is followed by a discussion of the HH OBC, which is applicable to non-dispersive media on cylindrical and spherical geometries. The paper extends this OBC to the "slightly dispersive" case.

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Section: Extension Of the Hagstrom -Hariharan Conditions To Dispersivmentioning

confidence: 99%

“…First, we recall the essential facts from Hagstrom and Hariharan (1998). The standard wave equation in either the 2D-cylindrical or 3D-spherical case is:…”

Section: Extension Of the Hagstrom -Hariharan Conditions To Dispersivmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

High-order Non-reflecting Boundary Conditions for Dispersive Waves in Cartesian, Cylindrical and Spherical Coordinate Systems

Joolen

Givoli

Neta

2003

International Journal of Computational Fluid Dynamics

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

Huan

Thompson

2000

Int. J. Numer. Meth. Engng.

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Asymptotic and exact local radiation boundary conditions (RBC) for the scalar time-dependent wave equation, ÿrst 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 ÿrstorder 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 ÿnite 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 highorder 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.

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Acoustics

Thompson

Pinsky

2004

Encyclopedia of Computational Mechanics

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State‐of‐the‐art computational methods for linear acoustics are reviewed. The equations of linear acoustics are summarized and then transformed to the frequency domain for time‐harmonic waves governed by the Helmholtz equation. Two major current challenges in the field are specifically addressed: numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales and requiring a large computational effort, and the effective treatment of unbounded domains by domain‐based methods. A discussion of the indefinite sesquilinear forms in the corresponding weak form are summarized. A priori error estimates, including both dispersion (phase error) and global pollution effects for moderate to large wave numbers in finite element methods, are discussed. Stabilized and other wave‐based discretization methods are reviewed. Domain‐based methods for modeling exterior domains are described including Dirichlet‐to‐Neumann (DtN) methods, absorbing boundary conditions, infinite elements, and the perfectly matched layer (PML). Efficient equation‐solving methods for the resulting complex‐symmetric (non‐Hermitian) matrix systems are discussed including parallel iterative methods and domain decomposition methods including the FETI‐H method. Numerical methods for direct solution of the acoustic wave equation in the time domain are reviewed.

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A formulation of asymptotic and exact boundary conditions using local operators

Cited by 155 publications

References 6 publications

High-order Non-reflecting Boundary Conditions for Dispersive Waves in Cartesian, Cylindrical and Spherical Coordinate Systems

High-order Non-reflecting Boundary Conditions for Dispersive Waves in Cartesian, Cylindrical and Spherical Coordinate Systems

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

Acoustics

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