Finite element formulation with high-order absorbing boundary conditions for time-dependent waves

Givoli, Dan; Hagstrom, Thomas; Patlashenko, Igor

doi:10.1016/j.cma.2005.01.021

Cited by 75 publications

(81 citation statements)

References 14 publications

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“…Our description below will follow [39]. We note that parallel developments for the scalar wave equation are reported in [40,24,37].…”

Section: 2mentioning

confidence: 99%

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Hagstrom¹,

Lau

2007

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Abstract. We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identfying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.

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“…Our description below will follow [39]. We note that parallel developments for the scalar wave equation are reported in [40,24,37].…”

Section: 2mentioning

confidence: 99%

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Hagstrom¹,

Lau

2007

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“…The boundary condition (5) is a Higdon BC [9] and coefficients a j ∈ (0, 1] are given parameters. Rewriting (5) according to the Hagstrom-Warburton formulation [10,14,15], adapted to the problem stated in the frequency domain, BC (5) becomes…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…In this work the Hagstrom-Warburton ABC [10,14] is chosen. The benefit of implementing nonreflecting BCs is discussed in [8] and it has been proven in [15] that the Hagstrom-Warburton ABC is equivalent to the popular Higdon ABC, with advantages with respect to implementation and computational cost.…”

Section: Introductionmentioning

confidence: 99%

Equivalent Boundary Conditions for Heterogeneous Acoustic Media

Castro

Diaz

Péron

2014

Tend. Mat. Apl. Comput.

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ABSTRACT. In this work, we derive high order Equivalent Absorbing Boundary Conditions EABCs that model the propagation of waves in semi-infinite bilayered acoustic media. Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. These EABCs are adapted to Hagstrom-Warburton ABCs and appear as first and second order of approximation with respect to a small parameter involved in a multiscale expansion. Computational tests illustrate the accuracy of the first approximate model with respect to the small parameter.

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“…Recently highorder ABCs which are local and involve no higher derivatives are also devised [7,37]. They are based on a high-order form of Higdon ABCs by using auxiliary variables [24,26,27,36].…”

Section: Introductionmentioning

confidence: 99%

Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations

Zhang

Chung

2014

Communications in Mathematical Sciences

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Abstract. Simulation of waves in complex poroelastic media is crucial in providing important geophysical information that cannot be obtained via simple elastic or acoustic models. Thus there is a need to design an artificial boundary condition for simulation using the numerical approximation of such a problem. In this paper, our aim is to derive an exact nonreflecting boundary condition for the three dimensional poroelastic wave equations based on the Grote-Keller method. The proposed boundary condition is nonlocal in space, but local in time and can be coupled easily with standard numerical approaches for the computation of numerical solutions. Numerical results computed by the finite difference method demonstrate the effectiveness of our method.

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Finite element formulation with high-order absorbing boundary conditions for time-dependent waves

Cited by 75 publications

References 14 publications

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Radiation Boundary Conditions for Maxwell's Equations: A Review of Accurate Time-Domain Formulations

Equivalent Boundary Conditions for Heterogeneous Acoustic Media

Exact nonreflecting boundary conditions for three dimensional poroelastic wave equations

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