Kazuhiro Koro

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.

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.

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.

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.