This paper presents an innovative method, called the mode-exciting method, to solve Lamb wave-scattering problems in an infinite plate. In this method, a set of Lamb wave modes is excited by appropriate boundary conditions given on the virtual edges of a finite plate. After solving numerically the elastodynamic problem defined in the finite domain, the numerical solution is decomposed into Lamb wave modes. The Lamb wave modes constitute a system of equations, which can be used to determine the scattering coefficients of Lamb waves for the original problem in an infinite plate. The advantage of the mode-exciting method is that a well-developed numerical method such as finite-element (FEM) or boundary element (BEM) can be used in the elastodynamic analysis for the finite region without any modification like coupling with other numerical techniques. In numerical examples, first the error estimation of the mode-exciting method is discussed by considering three types of error indicators. It is shown that among them, the power ratio of nonpropagating modes to propagating modes is the most suitable for the error estimation. Numerical results are then shown for scattering coefficients as a function of nondimensional frequency for edge reflection and crack scattering problems.

This paper analyzes the edge-reflection problem of obliquely incident guided waves in a plate. The generalized guided-wave theories in a plate, including the orthogonality of modes and the mode-decomposition method are summarized. The edge-reflection problem is solved on the basis of the mode-decomposition method. Some numerical results are presented and compared to experimental results.

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The fast multipole boundary element method (FMBEM), which is an efficient BEM that uses the fast multipole method (FMM), is known to suffer from instability at low frequencies when the well-known high-frequency diagonal form is employed. In the present paper, various formulations for a low-frequency FMBEM (LF-FMBEM), which is based on the original multipole expansion theory, are discussed; the LF-FMBEM can be used to prevent the low-frequency instability. Concrete computational procedures for singular, hypersingular, Burton-Miller, indirect (dual BEM), and mixed formulations are described in detail. The computational accuracy and efficiency of the LF-FMBEM are validated by performing numerical experiments and carrying out a formal estimation of the efficiency. Moreover, practically appropriate settings for numerical items such as truncation numbers for multipole/local expansion coefficients and the lowest level of the hierarchical cell structure used in the FMM are investigated; the differences in the efficiency of the LF-FMBEM when different types of formulations are used are also discussed.

Existing Scanning/Transmission Electron Microscopy (S/TEM) image simulation algorithms such as Multislice and Bloch Wave are based exclusively on elastic scattering. At thicker specimens inelastic scattering may affect image intensity and contrasts. Previous semi-quantitative incorporation of inelastic plasmon scattering into the output of Multislice simulated diffraction patterns has improved the agreement between experimental and simulation results from ~ 30 % to less than 10 % [1]. In this study, a full quantitative plasmon scattering algorithm was incorporated into multislice method [2] by allowing the wavefunction of the propagating beam to interact inelastically within each slice [3].Crystalline Si samples with 4 x 4 nm supercells oriented along <100> crystallographic direction with various thicknesses were used in this simulation. STEM operated at 100 kV accelerating voltage and 11.4 mrad convergence angle giving about 2 Å diameter probe was used here. High-angle annular darkfield (HAADF) STEM images and Electron Energy Loss Spectroscopy (EELS) signals were calculated. For HAADF-STEM images 54 -150 mrad detector was used and 20 mrad collection angles was used for EELS.The modified "inelastic-elastic" multislice method first takes into account the plasmon scattering by calculating the energy loss for each scattering angles before undergoing the elastic scattering through transmission operation. Then beam propagates to the next slice using propagation operator. Simulated EELS spectra in Si using new "inelastic-elastic" multislice method for thicknesses of 42, 74, 83, and 130 nm are shown in Figure 1 comparable with early experiments performed under similar conditions [4]. An energy dispersion of 1 eV (for energy loss up to 60 eV) was used in the simulation to monitor single, double, and triple plasmon scattering in these Si samples. A good agreement was achieved for the range of specimen thicknesses.