اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدA multi-frequency sampling method for the inverse source problems with sparse measurements
151
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We consider the inverse source problems with multi-frequency sparse near field measurements. In contrast to the existing near field operator based on the integral over the space variable, a multi-frequency near field operator is introduced based on the integral over the frequency variable. A factorization of this multi-frequency near field operator is further given and analysed. Motivated by such a factorization, we introduce a multi-frequency sampling method to reconstruct the source support. Its theoretical foundation is then derived from the properties of the factorized operators and a properly chosen point spread function. Numerical examples are provided to illustrate the multi-frequency sampling method with sparse near field measurements. Finally we briefly discuss how to extend the near field case to the far field case.
قيم البحث
اقرأ أيضاً
The randomized sparse Kaczmarz method was recently proposed to recover sparse solutions of linear systems. In this work, we introduce a greedy variant of the randomized sparse Kaczmarz method by employing the sampling Kaczmarz-Motzkin method, and pro
ve its linear convergence in expectation with respect to the Bregman distance in the noiseless and noisy cases. This greedy variant can be viewed as a unification of the sampling Kaczmarz-Motzkin method and the randomized sparse Kaczmarz method, and hence inherits the merits of these two methods. Numerically, we report a couple of experimental results to demonstrate its superiority
This paper investigates the inverse scattering problems using sampling methods with near field measurements. The near field measurements appear in two classical inverse scattering problems: the inverse scattering for obstacles and the interior invers
e scattering for cavities. We propose modified sampling methods to treat these two classical problems using near field measurements without making any asymptotic assumptions on the distance between the measurement surface and the scatterers. We provide theoretical justifications based on the factorization of the near field operator in both symmetric factorization case and non-symmetric factorization case. Furthermore, we introduce a data completion algorithm which allows us to apply the modified sampling methods to treat the limited-aperture inverse scattering problems. Finally numerical examples are provided to illustrate the modified sampling methods with both full- and limited- aperture near field measurements.
In this study, a multi-grid sampling multi-scale (MGSMS) method is proposed by coupling with finite element (FEM), extended finite element (XFEM) and molecular dynamics (MD) methods.Crack is studied comprehensively from microscopic initiations to mac
roscopic propagation by MGSMS method. In order to establish the coupling relationship between macroscopic and microscopic model, multi-grid FEM is used to transmit the macroscopic displacement boundary conditions to the atomic model and the multi-grid XFEM is used to feedback the microscopic crack initiations to the macroscopic model. Moreover, an image recognition based crack extracting method is proposed to extract the crack coordinate from the MD result files of efficiently and the Latin hypercube sampling method is used to reduce the computational cost of MD. Numerical results show that MGSMS method can be used to calculate micro-crack initiations and transmit it to the macro-crack model. The crack initiation and propagation simulation of plate under mode I loading is completed.
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame thresholdi
ng approach which we show to provide a convergent regularization method with linear convergence rates. These results will be compared to the well-known analysis and synthesis variants of sparse $ell^1$-regularization which are usually implemented thorough iterative schemes. If the frame is a basis (non-redundant case), the thr
We introduce a new method for the numerical approximation of time-harmonic acoustic scattering problems stemming from material inhomogeneities. The method works for any frequency $omega$, but is especially efficient for high-frequency problems. It is
based on a time-domain approach and consists of three steps: emph{i)} computation of a suitable incoming plane wavelet with compact support in the propagation direction; emph{ii)} solving a scattering problem in the time domain for the incoming plane wavelet; emph{iii)} reconstruction of the time-harmonic solution from the time-domain solution via a Fourier transform in time. An essential ingredient of the new method is a front-tracking mesh adaptation algorithm for solving the problem in emph{ii)}. By exploiting the limited support of the wave front, this allows us to make the number of the required degrees of freedom to reach a given accuracy significantly less dependent on the frequency $omega$, as shown in the numerical experiments. We also present a new algorithm for computing the Fourier transform in emph{iii)} that exploits the reduced number of degrees of freedom corresponding to the adapted meshes.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
