Kazuhisa Abe

Non-orthogonal spline wavelets for boundary element analysis

Non-orthogonal spline wavelets are developed for Galerkin boundary element method. The proposed wavelets have compact supports and closed-form expressions. Besides, one can choose arbitrarily the order of vanishing moments of the wavelets independently of order of B-splines. Sparse coefficient matrices are obtained by truncating the small elements a priori. The memory requirement and computational time can be controled by changing the order of vanishing moments of the wavelets. As an iterative technique for solving the boundary element equations, GMRES(m) method is employed. Diagonal scaling and incomplete LU factorization (ILU(0)) are considered for the preconditioning. The ILU(0) becomes an effective preconditioner for higher order vanishing moments. Through numerical examples, availability of the proposed wavelets is investigated.

A new residue and nodal error evaluation in h- adaptive boundary element method

Abstract An error indicator and evaluation of nodal error are proposed in the h -adaptive boundary element method. Error indicator is defined based on a new residue calculated at collocation points only. Nodal error is evaluated from the approximated residue by solving a matrix equation. Convergence of the solution is estimated with the nodal error. Efficiency of the proposed strategy is proved through numerical examples.

An h-hierarchical Galerkin BEM using Haar wavelets

Application of Haar wavelet to h-hierarchical adaptive method is attempted to improve the performance. The wavelet boundary element method (BEM) is developed by means of the Galerkin method. In order to save memory requirement and computation time, sparse matrices are obtained by truncation of matrix coefficients. Error indicator and estimator are constructed based on the difference between the true solution and its projection onto the mesh. These values are effectively evaluated using the boundary element solution. The adaptive method is developed for 2D Laplace problems. Through numerical examples, performance of the present method is investigated concerning the sparseness of matrices and the computation time devoted to calculation of matrix coefficients and to equation solving process.

An hr-adaptive boundary element for water free-surface problems

Abstract An hr-adaptive remeshing method is developed for nonlinear 2-D analysis of the free-surface on water. In order to approximate velocity potential and boundary conditions imposed on the free surface, boundary element method and weighted residual method are employed. Weighted average of error estimators of these two approximation methods is introduced on the free surface and unique optimum mesh is obtained based on the averaged-error estimator. In the proposed method, the role of h-process is to decide a priori the number of elements required to satisfy an error tolerance. Thus, the h-process has no need to select some elements which have poor accuracy, nor to refine these elements. Optimization of the element distribution is carried out by the r-process for the number of elements decided by the h-process. The proposed method is applied to sloshing in a rectangular container and forced oscillation in a trapezoidal container. Through these analyses, the performance and efficiency of the hr-method are investigated.

A wavelet method for reducing the computational cost of BE-based homogenization analysis

Abstract A wavelet BEM is applied to the evaluation of the effective elastic moduli of unidirectional composites, based on the homogenization theory. This attempt is devoted to the reduction of computational cost for the BE-based homogenization analysis. Truncation for matrix compression is carried out by the Beylkin-type algorithm. A thresholding value for the truncation is set such that the discretization error of BE solution is comparable to its truncation error. Besides, rearrangement of the BE equations is proposed to attain rapid convergence of iterative solutions. Through investigation of asymptotical convergence of the effective moduli, it is found that the BE-based homogenization analysis ensures the same rate of convergence for effective moduli as for characteristic functions. By applying the wavelet BEM to heterogeneous media which have microstructures with many voids, the effective moduli with agreement of 2–4 digits can be evaluated using 20–50% memory requirements of conventional BE approaches.

Application of Haar wavelets to time-domain BEM for the transient scalar wave equation

The time-domain boundary element method using the Haar wavelets is developed for reducing the computational cost of the BE wave propagation analysis. The Haar wavelets are used for the discretization of the boundary integral equation. The time variation of the unknown potential and flux is approximated using the conventional scheme. The small matrix entries of the coefficient matrix are truncated with the Beylkin-type matrix compression scheme at before and after calculation of double boundary integral. The present BEM has the numerical stability comparable to the piecewise constant Galerkin BEM. The sparsity of the coefficient matrix generated at an each time step rises as the time step proceeds; the memory requirement of the present method can be reduced in comparison with the conventional BEM. The reduction of the computational work from the conventional BE analysis is difficult because of the sparse system of the conventional time-domain BEM.

Level Set based Topological Shape Optimization of Phononic Crystals

A topology optimization method for phononic crystals is developed for the design of sound barriers, using the level set approach. Given a frequency and an incident wave to the phononic crystals, an optimal shape of periodic inclusions is found by minimizing the norm of transmittance. In a sound field including scattering bodies, an acoustic wave can be refracted on the obstacle boundaries, which enables to control acoustic performance by taking the shape of inclusions as the design variables. In this research, we consider a layered structure which is composed of inclusions arranged periodically in horizontal direction while finite inclusions are distributed in vertical direction. Due to the periodicity of inclusions, a unit cell can be considered to analyze the wave propagation together with proper boundary conditions which are imposed on the left and right edges of the unit cell using the Bloch theorem. The boundary conditions for the lower and the upper boundaries of unit cell are described by impedance matrices, which represent the transmission of waves between the layered structure and the semi-infinite external media. A level set method is employed to describe the topology and the shape of inclusions. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set function, which facilitates to handle complicated topological shape changes. Through several numerical examples, the applicability of the proposed method is demonstrated.

Roles and effects of human network of supporting experts out of Niigata University to practical engineering education

The educational supporting human network outside the university we call as “The Network of 100 Wise Men” has been constructed by Faculty of Engineering of Niigata University on the process of educational reform activities. We have operated various kinds of practical engineering programs which have been assisted by the engineers of companies and societies. The network members possess the actual experiences of engineering through the processes of their practical R&D activities. And the guidance, lectures, and advice by the network members have made a lot of beneficial contributions to the engineering education for the university students as well as to the faculties of Niigata University. The network is composed of various generations and industrial areas, which is not only based on the alumni organization but on the personal reliance between the faculties and engineers/scientists through their continueing research collaborations. We are convinced that it must be much advantageous for the university students to obtain the practical engineering skills and their ways of thinking by means of the cooperation of the network members.

Educational programs for freshmen based on forefront scientific researches on the environmental purification project with intense magnetic fields

University students before starting their graduation researches, including the freshmen grade students, have been participating in the forefront R&D projects. Since practical activities generally contain the educational elements for university students, we thought that the forefront collaboration projects conducted in private companies and universities must have been effective for the students to motivate their academic activities. The project called as the practical learn-by-doing program collaborated with the companies out of the university was adopted by the Japanese government, which started in 2005. In the process, twelve “Incubation projects” were conducted for five years. We refer to the environmental purification project with use of intense magnetic fields among them. This education program was taken over as one of the research themes in the novel educational reform activity called “Smart Dormitory” as a leadership program which started in 2012. The environmental purification project has been carried out by six undergraduate students including freshmen for two years. The students were motivated well to the research themes when the chances of presentations were given in their early stage of university life. They have joined five academic meetings held in domestic areas and overseas for two years to announce their research performances.

Sleeper Spacing Optimization for Vibration Reduction in Rails

In this study, a theoretical investigation of optimized sleeper spacing which can suppress resonances of a railway track is attempted. To achieve this, we introduced a minimization problem in which the objective function is given by the wave transmittance and the design variable is defined by sleeper distribution. In the analysis the rail is modeled by a Timoshenko beam and the sleeper is represented by a mass. The infinite track analysis is realized by attaching the transmitting boundaries at both ends of the finite optimization region. Through numerical analyses the sleeper spacing effective in reduction of the transmittance is discussed. Furthermore, the feasibility of the proposed method is validated in the aspect of vibration reduction through response analyses for a harmonic load.