scholarly journals The three dimensional weak form of the conjugate gradient FFT method for solving scattering problems

1992 ◽  
Vol 40 (9) ◽  
pp. 1757-1766 ◽  
Author(s):  
P. Zwamborn ◽  
P.M. van den Berg
Keyword(s):  
Conjugate Gradient ◽  
Three Dimensional ◽  
Weak Form ◽  
Scattering Problems

scholarly journals Heating source localization in a reduced time

2016 ◽  
Vol 26 (3) ◽  
pp. 623-640 ◽  
Author(s):  
Sara Beddiaf ◽  
Laurent Autrique ◽  
Laetitia Perez ◽  
Jean-Claude Jolly
Keyword(s):  
Heat Conduction ◽  
Source Localization ◽  
Conjugate Gradient ◽  
Regularization Method ◽  
Three Dimensional ◽  
Gradient Algorithm ◽  
Iterative Regularization ◽  
Heating Source ◽  
Ill Posed ◽  
Reduced Time

Abstract Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

scholarly journals Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems

2019 ◽  
Vol 5 (2) ◽  
pp. 27 ◽  
Author(s):  
Yu Zhong ◽  
Kuiwen Xu
Keyword(s):  
Integral Equation ◽  
Inverse Scattering ◽  
Contraction Mapping ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Optimization Method ◽  
Scattering Problems ◽  
Physical Reason ◽  
Inverse Scattering Problems ◽  
Highly Nonlinear

Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for inversion (CIE-I) has been proposed to tackle the two-dimensional electromagnetic ISPs, in which the usually employed Lippmann–Schwinger integral equation (LSIE) is transformed into a new form with a modified medium contrast via a contraction mapping. With the CIE-I, the multiple scattering effects, i.e., the physical reason for the nonlinearity in the ISPs, is substantially suppressed in estimating the modified contrast, without compromising physical modeling. In this paper, we firstly propose to implement this new CIE-I for the three-dimensional ISPs. With the help of the FFT type twofold subspace-based optimization method (TSOM), when handling the highly nonlinear problems with strong scatterers, those with higher contrast and/or larger dimensions (in terms of wavelengths), the performance of the inversions with CIE-I is much better than the ones with the LSIE, wherein inversions usually converge to local minima that may be far away from the solution. In addition, when handling the moderate scatterers (those the LSIE modeling can still handle), the convergence speed of the proposed method with CIE-I is much faster than the one with the LSIE. Secondly, we propose to relax the contraction mapping condition, i.e., different contraction mappings are used in updating contrast sources and contrast, and we find that the convergence can be further accelerated. Several numerical tests illustrate the aforementioned interests.

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