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Hongyu Liu

Publications and source records attributed to Hongyu Liu.

301 records · Page 17Linked to original sources
arXiv2013

Two Single-shot Methods for Locating Multiple Electromagnetic Scatterers

We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting plane wave. The first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave. The multiple scatterers could be extremely general with an unknown number of components, and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content. The second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting EM wavelength. The number of the obstacle components is not required to be known in advance, but the shape of each component must be from a certain known admissible class. The admissible class may consist of multiple different reference obstacles. The second scheme could also be extended to include the medium components if a certain generic condition is satisfied. Both schemes are based on some novel indicator functions whose indicating behaviors could be used to locate the scatterers. No inversion will be involved in calculating the indicator functions, and the proposed methods are every efficient and robust to noise. Rigorous mathematical justifications are provided and extensive numerical experiments are conducted to illustrate the effectiveness of the imaging schemes.

math.AP↗
arXiv2012

On Near-cloak in Acoustic Scattering

Invisibility cloaking in acoustic scattering via the approach of transformation optics is considered. The near-cloaks of both passive medium and active/radiating object are investigated. From a practical viewpoint, we are especially interested in the cloaking of an arbitrary (but regular) content. It is shown that one cannot achieve the near-cloak unless some special mechanism is introduced into the construction. A general lossy layer is incorporated into the construction of our near-cloaking devices. We derive very accurate estimates of the scattering amplitude in terms of the regularization parameter and the material parameters of the lossy layer in different settings.

math.AP↗
arXiv2012

Enhanced Near-cloak by FSH Lining

We consider regularized approximate cloaking for the Helmholtz equation. Various cloaking schemes have been recently proposed and extensively investigated. The existing cloaking schemes in literature are (optimally) within $|\lnρ|^{-1}$ in 2D and $ρ$ in 3D of the perfect cloaking, where $ρ$ denotes the regularization parameter. In this work, we develop a cloaking scheme with a well-designed lossy layer right outside the cloaked region that can produce significantly enhanced near-cloaking performance. In fact, it is proved that the proposed cloaking scheme could (optimally) achieve $ρ^N$ in $\mathbb{R}^N$, $N\geq 2$, within the perfect cloaking. It is also shown that the limit of the proposed lossy layer corresponds to a sound-hard layer. We work with general geometry and arbitrary cloaked contents of the proposed cloaking device.

math.AP↗
arXiv2012

Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space

In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft layer lining right outside the cloaked region, we show that one can achieve the near-invisibility by the `blow-up-a-small-region' construction. This is based on novel scattering estimates corresponding to small sound-soft obstacles located in isotropic space. One of the major novelties of our scattering estimates is that one cannot make use of the scaling argument in the setting of current study due to the simultaneous presence of asymptotically small obstacle components and regularly sized obstacle components, and one has to decouple the nonlinear scattering interaction between the small obstacle components and, the regular obstacle components together with the background medium.

math.AP↗
arXiv2012

Singular perturbation of reduced wave equation and scattering from an embedded obstacle

We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain $Ω\subset\mathbb{R}^N$ ($N\geq 2$). {In a subregion $D\SubsetΩ$, the medium is supposed to be lossy and have a large mass density. We study the asymptotic development of the wave field as the mass density $ρ\rightarrow +\infty$} and show that the wave field inside $D$ will decay exponentially while the wave filed outside the medium will converge to the one corresponding to a sound-hard obstacle $D\SubsetΩ$ buried in the medium supported in $Ω\backslash\bar{D}$. Moreover, the normal velocity of the wave field on $\partial D$ from outside $D$ is shown to be vanishing as $ρ\rightarrow +\infty$. {We derive very accurate estimates for the wave field inside and outside $D$ and on $\partial D$ in terms of $ρ$, and show that the asymptotic estimates are sharp. The implication of the obtained results is given for an inverse scattering problem of reconstructing a complex scatterer.}

math.AP↗
arXiv2011

Enhanced Approximate Cloaking by SH and FSH Lining

We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12] [17] for the Helmholtz equation. The cloaking schemes in [12] and [17] are shown to be (optimally) within $|\lnρ|^{-1}$ in 2D and $ρ$ in 3D of perfect cloaking, where $ρ$ denotes the regularization parameter. In this paper, we show that by employing a sound-hard layer right outside the cloaked region, one could (optimally) achieve $ρ^N$ in $\mathbb{R}^N,\ N\geq 2$, which significantly enhances the near-cloak. We then develop a cloaking scheme by making use of a lossy layer with well-chosen parameters. The lossy-layer cloaking scheme is shown to possess the same cloaking performance as the one with a sound-hard layer. Moreover, it is shown that the lossy layer could be taken as a finite realization of the sound-hard layer. Numerical experiments are also presented to assess the cloaking performances of all the cloaking schemes for comparisons.

math.AP↗
arXiv2010

On Approximate Electromagnetic Cloaking by Transformation Media

We give a comprehensive study on regularized approximate electromagnetic cloaking via the transformation optics approach. The following aspects are investigated: (i) near-invisibility cloaking of passive media as well as active/radiating sources; (ii) the existence of cloak- busting inclusions without lossy medium lining; (iii) overcoming the cloaking-busts by employing a lossy layer outside the cloaked region; (iv) the frequency dependence of the cloaking performances. We address these issues and connect the obtained asymptotic results to singular ideal cloaking. Numerical verifications and demonstrations are provided to show the sharpness of our analytical study.

math.AP↗
arXiv2010

Two dimensional invisibility cloaking via transformation optics

We investigate two-dimensional invisibility cloaking via transformation optics approach. The cloaking media possess much more singular parameters than those having been considered for three-dimensional cloaking in literature. Finite energy solutions for these cloaking devices are studied in appropriate weighted Sobolev spaces. We derive some crucial properties of the singularly weighted Sobolev spaces. The invisibility cloaking is then justified by decoupling the underlying singular PDEs into one problem in the cloaked region and the other one in the cloaking layer. We derive some completely novel characterizations of the finite energy solutions corresponding to the singular cloaking problems. Particularly, some `hidden' boundary conditions on the cloaking interface are shown for the first time. We present our study for a very general system of PDEs, where the Helmholtz equation underlying acoustic cloaking is included as a special case.

math.AP↗
arXiv2008

Virtual reshaping and invisibility in obstacle scattering

We consider reshaping a scattering obstacle virtually by using transformation optics in acoustic and electromagnetic scattering. Among the general virtual reshaping results, the virtual minification and virtual magnification are particularly studied. Stability estimates are derived for scattering amplitude in terms of the diameter of a small obstacle, which implies that the limiting case for minification corresponds to a perfect cloaking, i.e., the obstacle is invisible to detection.

physics.optics↗
arXiv2008

Recovery of inhomogeneities and buried obstacles

In this paper we consider the unique determination of inhomogeneities together with possible buried obstacles by scattering measurements. Under the assumption that the buried obstacles have only planar contacts with the inhomogeneities, we prove that one can recover both of them by knowing the associated scattering amplitude at a fixed energy.

math.AP↗
arXiv2008

Preservation of stability properties near fixed points of linear hamiltonian systems by symplectic integrators

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.

math.NA↗