Monte Carlo simulation via a numerical algorithm for solving a nonlinear inverse problem

AbstractThe coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.

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Reconstruction of a Robin Coefficient by a Predictor-Corrector Method

Mathematical Problems in Engineering ◽

10.1155/2015/496587 ◽

2015 ◽

Vol 2015 ◽

pp. 1-7

Author(s):

Yun-Jie Ma

Keyword(s):

Inverse Problem ◽

Approximate Solution ◽

Temperature Measurement ◽

Numerical Algorithm ◽

Nonlinear Inverse Problem ◽

Boundary Temperature ◽

Predictor Corrector

The present paper is devoted to solving a nonlinear inverse problem of identifying a Robin coefficient from boundary temperature measurement. A numerical algorithm on the basis of the predictor-corrector method is designed to restore the approximate solution and the performance of the method is verified by simulating several examples. The convergence with respect to the amount of noise in the data is also investigated.

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Electron Scattering in Solids

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100133618 ◽

1990 ◽

Vol 48 (2) ◽

pp. 4-5

Author(s):

Ryuichi Shimizu ◽

Ze-Jun Ding

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Angular Distribution ◽

Elastic Scattering ◽

Electron Scattering ◽

Cross Sections ◽

Expansion Method ◽

Electron Excitation ◽

Partial Wave Expansion ◽

Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

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Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134922 ◽

1990 ◽

Vol 48 (2) ◽

pp. 264-265

Author(s):

D. R. Liu ◽

S. S. Shinozaki ◽

R. J. Baird

Keyword(s):

Thin Film ◽

Thin Films ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Compound Semiconductors ◽

Energy Dispersive Analysis ◽

X Ray ◽

Metastable Alloys ◽

Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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