Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation

Grote, Marcus J.; Keller, Joseph B.

doi:10.1137/s0036139993269266

Cited by 194 publications

(157 citation statements)

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“…Hagstrom and Hariharan [5] proposed a high-order asymptotic NRBC for two-dimensional domains. Additionally, they, along with Grote and Keller [6], constructed exact NRBCs for three-dimensional waves where B is a sphere.…”

Section: Introductionmentioning

confidence: 99%

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

Neta

Joolen

Dea

et al. 2007

Commun. Numer. Meth. Engng.

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SUMMARYA shallow water model with linear time-dependent dispersive waves in an unbounded domain is considered. The domain is truncated with artificial boundaries B where a sequence of high-order non-reflecting boundary conditions (NRBCs) proposed by Higdon are applied. Methods devised by Givoli and Neta that afford easy implementation of Higdon NRBCs are refined in order to reduce computational expenses. The new refinement makes the computational effort associated with the boundary treatment quadratic rather than exponential (as in the original scheme) with the order. This allows for implementation of NRBCs of higher orders than previously. A numerical example for a semi-infinite channel truncated on one side is presented. Finite difference schemes are used throughout.

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Section: Introductionmentioning

confidence: 99%

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

Neta

Joolen

Dea

et al. 2007

Commun. Numer. Meth. Engng.

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“…This boundary condition is a nonlocal operator and can be approximated by local boundary conditions [13], [7], [21] or fast evaluated [8], [2], [9]. One can also replace the boundary condition by a reflectionless sponge layer damping propagating waves [3].…”

Section: Introductionmentioning

confidence: 99%

A nonlinear approach to absorbing boundary conditions for the semilinear wave equation

Szeftel

2006

Math. Comp.

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“…Another example of applications of time-dependent Mie formulation includes an exact nonreflection global boundary condition [54,55] for partial differential equation based simulation. That is straightforward in time-harmonic case.…”

Section: Discussionmentioning

confidence: 99%

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

Shanker²

2015

PIER

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Abstract-Canonical solutions to frequency domain Maxwell's equations, in the spherical coordinate system, have found extensive use as is evident from citations in the scientific literature. What is conspicuous by its absence is lack of such expressions for transient Maxwell systems. The existence of such expressions or approximations, provide the means to glean interesting physics in a variety of applications as well as validate existing numerical fullwave solvers. However, developing these expressions is beset with challenges; direct inverse Fourier transforms of frequency domain expressions are unstable. Successful approaches that ameliorate this instability are more recent endeavor. In this paper, we generalize our earlier contribution to this effort by exploiting a novel representation of the retarded potential to derive expressions for scattering from a dielectric sphere. Several results are provided that demonstrate the stability and accuracy of the method.

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Exact Nonreflecting Boundary Conditions for the Time Dependent Wave Equation

Cited by 194 publications

References 3 publications

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

Application of high‐order Higdon non‐reflecting boundary conditions to linear shallow water models

A nonlinear approach to absorbing boundary conditions for the semilinear wave equation

Time-Dependent Lorentz-Mie-Debye Formulation for Electromagnetic Scattering From Dielectric Spheres (Invited Paper)

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