Nonreflecting boundary condition for time-dependent multiple scattering

Grote, Marcus J.; Kirsch, Christoph

doi:10.1016/j.jcp.2006.06.007

Cited by 31 publications

(30 citation statements)

References 30 publications

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“…This fact was independently exploited by Sofronov [63,64] and Grote and Keller [28,29,30] to derive and implement accurate temporally local conditions. (See also [31] for applications to multiple scattering.) In fact, in [38] it is shown that purely local conditions can be developed which are exact for solutions described by finitely many spherical harmonics.…”

Section: 22mentioning

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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Section: 22mentioning

confidence: 99%

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

Hagstrom¹,

Lau

2007

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“…Moreover, if we require that supp{u 1 } ⊂ Ω 1 and supp{u 2 } ⊂ Ω 2 at t = 0, u 1 and u 2 are uniquely defined for all time (see [18]). At x = B 1 , an exact NRBC is…”

Section: The One-dimensional Casementioning

confidence: 99%

On local nonreflecting boundary conditions for time dependent wave propagation

Grote

Sim

2009

Chin. Ann. Math. Ser. B

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The simulation of wave phenomena in unbounded domains generally requires an artificial boundary to truncate the unbounded exterior and limit the computation to a finite region. At the artificial boundary a boundary condition is then needed, which allows the propagating waves to exit the computational domain without spurious reflection. In 1977, Engquist and Majda proposed the first hierarchy of absorbing boundary conditions, which allows a systematic reduction of spurious reflection without moving the artificial boundary farther away from the scatterer. Their pioneering work, which initiated an entire research area, is reviewed here from a modern perspective. Recent developments such as high-order local conditions and their extension to multiple scattering are also presented. Finally, the accuracy of high-order local conditions is demonstrated through numerical experiments.

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“…For a review, see for example [5], [6], [7]. All these papers, except for [12], Sections 5.5, 5.6, [8], [9], [2], deal with the construction of NRBC with the property of absorbing only outgoing waves, not waves that are either outgoing or incoming. Therefore, known sources must necessarily be included in the computational domain.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the NRBC holds only for a single convex artificial boundary having a special shape, like a circle (sphere) or ellipse (ellipsoid). Only in the last years multiple scattering problems have been examined (see [8], [9]). Very recently, in ([2]) we have proposed a (fully) non local NRBC, based on a boundary integral relationship.…”

Section: Introductionmentioning

confidence: 99%

A Fictitious Domain Approach for Wave Propagation Problems in Unbounded Domains

Falletta¹,

Monegato²

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. We consider the scattering of waves by an obstacle O ⊂ R 2 having a sufficiently smooth boundary Γ. By using a fictitious domain approach, we artificially extend the solution inside the obstacle O. Then we solve the original problem in the simpler domain that includes O and that is artificially bounded by a perfectly transparent boundary B, delimiting the region of interest. We prescribe on B a Non Reflecting Boundary Condition (NRBC) which is based on a space-time integral equation and that defines a relationship that the solution of the differential problem and its normal derivative must satisfy on B (see [2]). Further, we enforce the Dirichlet boundary condition on Γ in a weak sense, by means of Lagrange multipliers. The NRBC is discretized on B by combining a special second order (in time) convolution quadrature and a standard collocation method in space. In the enlarged domain, this discretization is coupled with an unconditionally stable ODE time integrator and a FEM in space. The constraint on Γ is imposed by a matrix B h that represents a discrete trace operator.A particularly useful application of this approach is the scattering of a wave by rotating rigid bodies. In this case the method avoids the complexity of constructing at each time step a new finite element computational mesh and requires only the construction of the discrete trace operator B h . We present some results we have obtained for rotating (even multiple) scatterers and non trivial data. 959

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Nonreflecting boundary condition for time-dependent multiple scattering

Cited by 31 publications

References 30 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

On local nonreflecting boundary conditions for time dependent wave propagation

A Fictitious Domain Approach for Wave Propagation Problems in Unbounded Domains

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