Method For Scattering Problems Research Articles

Theoretical Study on Non-Improvement of the Multi-Frequency Direct Sampling Method in Inverse Scattering Problems

Generally, it has been confirmed that applying multiple frequencies guarantees a successful imaging result for various non-iterative imaging algorithms in inverse scattering problems. However, the application of multiple frequencies does not yield good results for direct sampling methods (DSMs), which has been confirmed through simulation but not theoretically. This study proves this premise theoretically by showing that the indicator function with multi-frequency can be expressed by the Bessel and Struve functions and the propagation direction of the incident field. This is based on the fact that the indicator function with single frequency can be expressed by the exponential and Bessel function of order zero of the first kind. Various simulation outcomes are shown to support the theoretical result.

A PML Finite Element Method for Electromagnetic Scattering Problems in a Two-Layer Medium

A PML Finite Element Method for Electromagnetic Scattering Problems in a Two-Layer Medium

Comparative Analysis of Different Preconditioning Methods in Electromagnetic Scattering Problems using MoM-FMM

The numerical solution of the electric field integral equation in electromagnetic scattering problems involving metallic bodies, using the method of moments in conjunction with the fast multipole method, gives rise a full matrix with highly spread complex eigenvalues and consequently with a low condition number. Thus, iterative methods may not converge or it will require an extremely large number of iterations, which make this strategy unfeasible due to the high solution time and the expensive computational resources required. To overcome this drawback, the system matrix must be preconditioned to ensure the convergence in a reasonable number of iterations and with appropriate accuracy. In this work, some preconditioning techniques are revised and applied to a linear equation system derived from such type of problems, and the performance of these preconditioners is estimated and analyzed comparatively using the generalized minimal residual iterative method.

An Adaptive Perfectly Matched Layer Method for Multiple Cavity Scattering Problems

AbstractA uniaxial perfectly matched layer (PML) method is proposed for solving the scattering problem with multiple cavities. By virtue of the integral representation of the scattering field, we decompose the problem into a system of single-cavity scattering problems which are coupled with Dirichlet-to-Neumann maps. A PML is introduced to truncate the exterior domain of each cavity such that the computational domain does not intersect those for other cavities. Based on the a posteriori error estimates, an adaptive finite element algorithm is proposed to solve the coupled system. The novelty of the proposed method is that its computational complexity is comparable to that for solving uncoupled single-cavity problems. Numerical experiments are presented to demonstrate the efficiency of the adaptive PML method.

Fully Coupled Multi-Hybrid Finite Element Method–Method of Moments–Physical Optics Method for Scattering and Radiation Problems

A general fully coupled multi-hybrid method in three dimensions combining the finite element method, the method of moments, and a high-frequency asymptotic technique, namely, physical optics, is presented. Complex radiating structures are analyzed with finite element method (which easily handles complex geometries, permeable materials, anisotropy, and so on), while small- and medium-sized perfect electric conductor objects are rigorously analyzed using the method of moments; large perfect electric conductor objects can be efficiently analyzed with physical optics. Furthermore, different regions of the same object can be modeled with the method of moments and physical optics. Several numerical results are presented showing the validity of the method.

A Generalized Mode Matching Method for Scattering Problems with Unbounded Obstacles

Journal of Computational AcousticsVol. 09, No. 04, pp. 1611-1631 (2001) ICTCA'99 PapersNo AccessA GENERALIZED MODE MATCHING METHOD FOR SCATTERING PROBLEMS WITH UNBOUNDED OBSTACLESA.-S. BONNET-BENDHIA and A. TILLEQUINA.-S. BONNET-BENDHIAENSTA, SMP, URA 853-CNRS, 32 bd Victor, 75739 PARIS Cedex 15, France Search for more papers by this author and A. TILLEQUINENSTA, SMP, URA 853-CNRS, 32 bd Victor, 75739 PARIS Cedex 15, France Search for more papers by this author https://doi.org/10.1142/S0218396X01001005Cited by:5 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractThe two-dimensional time-harmonic acoustic scattering by a semi-infinite waveguide composed of two parallel rigid plates is considered. An original mode matching method is developed to avoid the use of the Wiener–Hopf technique, generalizing usual mode matching methods to the case of unbounded media. A brief description of the method is given by means of Fourier decomposition leading to a well-posed variational problem with unknown being the trace of the solution on a well-chosen interface.From the numerical point of view, a local approximation is first considered by using Lagrange P1 finite elements on a segment of the interface. This leads to the computation of oscillatory integrals involving Fourier transform and complex square root functions. As a matter of accuracy, a special function is added to the finite element space, in order to take into account the asymptotic behavior of the solution. Finally, this method is extended to deal with local perturbations of the media by coupling the previous method to a classical integral one.Presented at ICTCA'99, the 4th International Conference on Theoretical and Computational Acoustics, May 1999, Trieste, Italy. FiguresReferencesRelatedDetailsCited By 5Amplitude reflections and interaction solutions of linear and nonlinear acoustic waves with hard and soft boundariesMuhammad Ishaq and Zhi-Min Chen1 Nov 2022 | Physics of Fluids, Vol. 34, No. 11Mathematical Analysis of Wave Radiation by a Step-Like SurfaceWangtao Lu29 April 2021 | SIAM Journal on Applied Mathematics, Vol. 81, No. 2The halfspace matching method: A new method to solve scattering problems in infinite mediaAnne-Sophie Bonnet-Ben Dhia, Sonia Fliss and Antoine Tonnoir1 Aug 2018 | Journal of Computational and Applied Mathematics, Vol. 338Electromagnetic Wave Scattering from Rough Penetrable LayersHoussem Haddar and Armin Lechleiter1 Jan 2011 | SIAM Journal on Mathematical Analysis, Vol. 43, No. 5Solvability of singular integral system connected with seismic waves around the boreholeLeïla Alem and Lahcène Chorfi1 January 2006 | Mathematical Methods in the Applied Sciences, Vol. 29, No. 16 Recommended Vol. 09, No. 04 Metrics History Received 16 September 1999 Revised 6 June 2000 PDF download

Stable Coupling Method for Interface Scattering Problems by Combined Integral Equations and Finite Elements

The problem of elastic-fluid scattering is studied by combined integral equations for the exterior acoustic fluid and finite element methods for the elastic structure. These yield reduced problems over finite domains. The well-known difficulty with exterior integral equation methods at critical frequencies carries over to the reduced problem. A procedure is given to overcome this difficulty and a complete analysis of this procedure is provided, showing existence, uniqueness, and optimal convergence for the coupled problems. This method is termed stable. Numerical experiments confirm that the new approach is valid for all frequencies and indicate that variational methods are preferable to collocation in the treatment of integral equations, even for purely exterior problems. Our method is fully variational and may be expressed in a symmetric form.

The Effectiveness of Variational Methods for Inelastic Scattering Problems

The calculation of a partial cross section in atomic collision theory requires the solution of a pair of coupled integro-differential equations when the collision is inelastic and there is a possibility of particle exchange. A discussion is given of some variational procedures available for obtaining approximate solutions of such equations. These procedures are applied to the solution of two sets of model equations which simulate the equations of real problems but permit of exact solution. A comparison of exact and variational solutions enables the effectiveness of the variational methods to be assessed. It is found that a good approximation may be expected when trial functions are used which allow for the mixing of inelastically and elastically scattered waves, but that if only crude trial functions are used the approximation will be poor in cases where coupling is strong.