Sohichi Hirose

Parallelized fast multipole BEM based on the convolution quadrature method for 3-D wave propagation problems in time-domain

This paper presents a new time-domain boundary element method (BEM) using a convolution quadrature method (CQM) and a fast multipole method (FMM) in 3-D scalar wave propagation. In general, the use of direct time-domain BEM sometimes causes the numerical instability of time-stepping solutions and needs much computational time and memory. To overcome these difficulties, in this paper, the convolution quadrature method developed by Lubich is applied to establish the stability behavior of the time-stepping scheme. Moreover, the fast multipole method and parallelization techniques are adapted to improve the computational efficiency for large size problems. The formulation and numerical implementation of the new boundary element method, and the basic formulas for the fast multipole method such as the multipole expansion, the local expansion, and the translation relations of them in the fast multipole algorithm are presented. The accuracy, the computational efficiency and the applicability are checked by solving 3-D large scale wave scattering problems.

Application of Fast Multipole Boundary Element Method to Multiple Scattering Analysis of Acoustic and Elastic Waves

A fast multipole boundary element method (FMBEM) is developed for multiple scattering of 2‐D elastic and 3‐D acoustic waves. In the numerical calculation for 2‐D multiple scattering of elastic waves, reflection and transmission coefficients are obtained as a function of the wave number for the periodically distributed inclusions in the direction perpendicular to the incident wave propagation direction. In addition, numerical results for 3‐D multiple scattering of acoustic waves are demonstrated with considering the accuracy and computational efficiency of FMBEM.

COMPARATIVE STUDY ON ULTRASONIC IMAGING METHODS WITH ARRAY TRANSDUCERS

The performance of ultrasonic imaging methods developed in time domain and frequency domain algorithms is investigated in this study. The sectorial synthetic aperture focusing technique (S–SAFT) outputs the flaw image by superposing the sector–scan images obtained at various measurement points in the time domain. The inverse scattering imaging method (ISIM) is based on the elastodynamic inversion in the frequency domain and reconstructs the mathematical function which represents the flaw shape. The advantages and usabilities of these methods are discussed, taking into account the practical application to the NDE field.

Fast Imaging of 3‐D Flaw Using Linearized Inverse Scattering Methods

A high‐speed analysis of three‐dimensional linearized inverse scattering method is proposed for real time imaging of flaws. The principal operation of the linearized inverse method is the integration of the scattering amplitude in the K‐space. In this study, the three‐dimensional fast Fourier transform is introduced into the inversion algorithm to evaluate the integral in the K‐space. From the results of numerical investigations, it is shown that the computational time of the inversion is reduced without the loss of the image quality for the shape reconstruction.

3‐D Flaw Imaging by Inverse Scattering Analysis Using Ultrasonic Array Transducer

Ultrasonic matrix array transducers have the advantage of receiving flaw echoes simultaneously at various points on a flat surface of the test material. Here we propose 3‐D imaging techniques to reconstruct flaw shapes with the array transducer. These techniques are based on linearized inverse scattering methods in the frequency domain. The principal operation of these methods is the integration of the wave data in the K‐space. In this study, the 3‐D fast Fourier transform is introduced into the inversion algorithm to evaluate the integral in the K‐space. Performance of the 3‐D imaging technique is demonstrated by using the numerically calculated waveforms by the fast multipole BEM.

Interface Crack in Anisotropic Solids under Impact Loading

In this paper, transient dynamic crack analysis in two-dimensional, layered, anisotropic and linear elastic solids is presented. For this purpose, a time-domain boundary element method (BEM) is developed. The homogeneous and anisotropic layers are modeled by the multi-domain BEM formulation. Time-domain elastodynamic fundamental solutions for linear elastic and anisotropic solids are applied in the present BEM. The spatial discretization of the boundary integral equations is performed by a Galerkin-method while a collocation method is implemented for the temporal discretization of the arising convolution integrals. An explicit time-stepping scheme is developed to compute the discrete boundary data and the crack-opening-displacements (CODs). To show the effects of the material anisotropy and the dynamic loading on the dynamic stress intensity factors, numerical examples are presented and discussed.

Improved ultrasonic SAFT imaging of flaws in structures with curved surfaces

A time domain synthetic aperture focusing technique (SAFT) for flaw imaging of immersed structures with curved surfaces is improved in conjunction with approximate wave solutions, which were obtained in an explicit form by Schmerr (1998). In the improved SAFT, the approximate solutions are used to normalize A-scan waveforms and then the normalized waveforms are superimposed to obtain images with high contrast for a flaw in a structure in curved surfaces. As examples, the proposed SAFT is applied to experimental data for a side drilled hole (SDH) in an immersed round bar.

Large‐Scale Multiple Scattering Analysis Using Fast Multipole BEM in Time‐Domain

This paper presents a new fast multipole boundary element method (FMBEM) for multiple scattering analyses in time‐domain. The conventional time‐domain BEM has two disadvantages: 1) The numerical instability in time stepping procedure, and 2) much computational time and memory. Our proposed method overcomes these two disadvantages using the convolution quadrature method for 1) and the fast multipole method for 2). As numerical examples, the large‐scale multiple scattering of SH waves by many inclusions is conducted by the proposed method in this paper.

BEM Analysis of wave propagation in a water-filled borehole in an anisotropic solid

Abstract This paper describes a time-domain boundary element method developed to analyze the interactions of acoustic and elastic waves near the interfaces between water and an anisotropic elastic solid. Two models are analyzed with one being the interface between two half spaces of fluid and solid and the other being a fluid region sandwiched by half space domains of anisotropic elastic solids. Both monopole and dipole point sources are used to generate an initial pressure wave in the fluid. Some snapshots of the transient wave behavior near the fluid-solid interfaces are given. The effect of the anisotropy in the solid on the pressure waveforms in the fluid is discussed. The numerical results allow detailed arrival identification and interpretation of acoustic and elastic waves propagating along the fluid-solid interfaces.

A 3D boundary integral equation method for ultrasonic scattering in a fluid-loaded elastic half space

This paper presents a boundary integral equation method for 3D ultrasonic scattering problems in a fluid-loaded elastic half space. Since full scale of numerical calculation using finite element or boundary element method is still very expensive, we formulate a boundary integral equation for the scattered field, which is amenable to numerical treatment. In order to solve the problem using the integral equation, however, the wave field without scattering objects, so-called free field need to be given in advance. We calculate the free field by the plane wave spectral method where the asymptotic approximation is introduced for computational efficiency. To show the efficiency of our method, scattering by a spherical cavity near fluid-solid interface is solved and the validity of the results is discussed.