Ikuo Kaji

Lagrangian dual coordinatewise maximization algorithm for network transportation problems with quadratic costs

This paper gives the Lagrangian dual coordinatewise maximization (LDCM) algorithm for network transportation problems with strictly convex quadratic costs (NTPQ). An explicit expression for the dual function associated with NTPQ is obtained. Some properties of the dual function are shown. Then, using these properties, a procedure which involves successively maximizing the dual function with respect to each of its dual coordinates is applied to obtain the optimal dual solution. Then the optimal primal solution is obtained by substituting the dual solution to the simple expression. Computational results for 200 randomly generated problems reveal the effectiveness of the algorithm. The key idea of applying the Lagrangian dual method to NTPQ is that the objective function of the network problems is strictly convex. This strict convexity allows one to finesse problems that occur in using Lagrangian methods with more general problems. In particular, because the optimal solution of the Lagrangian problem is unique, the dual function is differentiable and an optimal solution to the Lagrangian with optimal multipliers is optimal in the original primal problem. These are strong results that are not true in general.

On mixed boundary element solutions of convection-diffusion problems in three dimensions

Abstract Three-dimensional boundary element solutions of steady convection-diffusion problems are presented. Numerical properties such as stability and accuracy on boundary element solutions based on a discretization using mixed boundary elements are compared with those of constant elements. It is found that boundary element solutions are unconditionally stable in space, nd that their relative errors to exact solutions hardly depend on the Pecler number. These results prove that the boundary element method is superior to domain-type numerical techniques which have a criterion of numerical stability and whose approximate solutions depend to some extent on the Pecelet number. The advantage of BEM using mixed elements, as compared with constant element solutions is also shown.

Correction procedures for flexible interpretive structural modeling

Flexible interpretive structural modeling (FISM) is an extended and improved version of the interpretive structural modeling developed by J.N. Warfield (1974). The computer algorithm of FISM is based on the partially filled reachability matrix (PR matrix) model, an extension of the reachability matrix (R matrix) model that has great utility in all phases of ISM. While an FISM structural model is being developed, or after it has been developed, the developer may want to make changes (corrections) in it. Several types of corrections for FISM are defined: change of one or more entries from zero to one; change of one or more entries from one to zero; deletion of one or more elements and their connections; and addition of one or more elements and their connections. Four tuned-up correction procedures are proposed to provide effective and consistent corrections. The correction procedures, along with the implication procedures for a PR-matrix, give a complete set of procedures for implementing FISM. >

Modular term rewriting systems and the termination

We present a novel approach to modularity. Rather than considering the union (direct sum) of the sets of rewrite rules, we consider the family (set) of them, introducing a new reduction called a modular reduction

Implication Theory and Algorithm for Reachability Matrix Model

A reachability matrix M is a binary matrix with the reflexive and transitive property, i.e., M + I = M, and M2 = M, where I is the identity matrix. The entries of the matrix M are shown to form a multilevel implication structure derived using the transitivity property. The fundamental implication matrix P that defines this structure is derived. The matrix Q of the transitive closure of P, the complete implication matrix, is defined. It is proved that Q = p2. The problem of efficiently filling the partially filled reachability matrix is considered. An algorithm for determining all of the implied values of the unknown elements of the partially filled reachability matrix M derived from a supplied value is proposed. The algorithm requires 0(n2) computer time and 0(n2) storage, where n is the size of the matrix M. Use of the algorithm to the interpretive structural modeling (ISM) process makes it possible to do a flexible and an efficient transitive embedding.

A Boundary-Element Analysis of TEM Cells in Three Dimensions

Transverse electromagnetic (TEM) transmission-line cells are modeled and analyzed in three dimensions based on a mixed discretization using both constant and linear boundary elements. In particular, the distributed characteristic impedance along the line is evaluated for symmetrical square TEM cells of the type built at the National Bureau of Standards (NBS) in order to confirm the validity of the present numerical technique. Comparison with experimental results is shown. This paper shows that our numerical approach should contribute to TEM cell design.

An analysis of nonlinear MHD equilibria of compact tori by using boundary element method

Magnetohydrodynamic (MHD) equilibria of an axisymmetric compact torus with a fixed boundary are analyzed using the boundary element method (BEM). An iterative method is used to obtain nonlinear solutions and study the effects of the injecting part of plasma and a center conductor. Both the force-free and the rigid drift configuration are analyzed, and the magnetic flux for the numerical model of the CTCC-I spheromak device at Osaka University (Japan) is calculated. It is shown that the BEM is useful to study nonlinear configurations of a compact torus. >

Regular boundary element solutions to steady-state convective diffusion equations

Abstract Regular boundary element method (R-BEM) is applied to analyse convective diffusion equations which are considered as governing equations of both steady-state heat-flow and travelling magnetic field problems. We consider a three-dimensional cubic model with Dirichlets boundary condition as a simple example in order to study stability and accuracy of regular boundary element (R-BE) solutions. It is found that R-BE solutions are unconditionally stable and their relative errors almost never depend on the location of source points. Furthermore, we can show that R-BE solutions have second-order accuracy as well as conventional BE solutions. Finally, numerical precision is studied through the condition number of the system matrices used in the analysis for a few parameters. It is shown that the R-BEM is available for the analysis of three-dimensional steady-state convective diffusion equations.

Nonlinear analysis of MHD equilibria of toroidal plasmas using boundary element method

Abstract Boundary element method (BEM) is applied to solve the nonlinear fixed boundary problem of magnetohydrodynamic (MHD) equilibria of toroidal plasmas. We first study linear BEM solutions with a square cross section as the initial profile in the iterative process by using two numerical models, and obtain the solutions with a good accuracy. Furthermore, we confirm convergence of weak nonlinear solutions using a simple iteration method and a successive three-step approximation method. Finally, we analyse weak nonlinear configurations for both several plasma and shape parameters. It is shown that BEM is useful for the nonlinear analysis of MHD equilibria.

An efficient procedure for transitive coupling in ISM

Transitive coupling is a procedure encountered in structuring complex systems using interpretive structural modeling (ISM). It involves the interconnection of two subsystems defined on the same contextual relation that is transitive. An efficient procedure or transitive coupling is proposed. The procedure presented is highlighted by savings in computer time and storage and by ease of programming. For a given value of one or zero for an unknown xij or yij, all inferences can be drawn with O(mn) computer time and θ((m+n)2) storage. Sufficient results obtained by a computer experiment using randomly generated problems are in close agreement with the results of the theoretical analysis.