Mechanical properties of ultra high molecular weight polyethylene (UHMWPE) used as a bearing material in total joint replacements have been investigated under impact compressive load. Cylindrical specimens, 5.3mm in both diameter and length, were cored from UHMWPE tibial inserts of two kinds of total knee replacement systems. Impact compression tests were performed using the split-Hopkinson pressure-bar (SHPB) method to determine dynamic Young's modulus. Viscoelastic characterization of UHMWPE based on the method developed by the authors showed that the three-element solid model, which consists of a serial spring E₁ and dashpot η connected in parallel with a second spring E₂, was applicable to both UHMWPE inserts.

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Effects of thermal cycling on tensile properties of SiC particulate reinforced cast aluminum alloy were studied and the results were discussed in terms of a fracture mechanism at the matrix alloy and particle for the tensile frature. The ductilities of thermally cycled material are twice larger than that of as received material. Measurements of 3D shape of the frature surfaces show that the SiC particle/matrix interface debonding occured around the SiC particle clusters in the case of thermally cycled specimen. A change of micromechanism of tensile fracture controls the ductility of Al/SiCp MMCs. The stress-strain behavoirs predicted based on a micromechanics model are consistent with the experimental results.

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The effects of crack face boundary conditions of the piezoelectric fracture mechanics are discussed by analyzing the plane strain electroelastic problem of an orthotropic piezoelectric ceramic strip with a central permeable or impermeable crack. The problem of a long strip is formulated by means of integral transforms and reduced to the solution of a system of Fredholm integral equations of the second kind. Fracture mechanics parameters such as stress intensity factor, energy release rate and energy density factor based on both permeable model and impermeable model are compared. A finite element method is also used to calculate these fracture mechanics parameters, and the results are compared with the exact solutions. The numerical results illustrate that the impermeable assumption can lead to significant errors regarding the effects of the electric fields on crack propagation.

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The purpose of the present paper is to obtain an accurate solution for the stress around the corner point of a semi-infinite strip with displacement constraints. A semi-infinite elastic strip fixed to rigid bodies on both sides is considered herein. Stress concentration with singularity occurs at the corner point on the free edge of the strip. The solution for the middle region along the free edge and the solution near the corner point are connected using the Lagrange multiplier method. The former solution is obtained via series expansion of eigenfunctions and the latter is obtained via the method of Goursat's complex stress functions. A solution of satisfactory accuracy is obtained over the entire range of the free edge, including the corner point.

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This paper presents the study on vibration and buckling of a clamped elliptical plate supported by a well-known Winkler-type foundation and subjected to a uniform in-plane force along the plate edge according to the ordinary thin plate theory. The analysis is rigorously made by the use of the Mathieu function and the modified Mathieu function, which appear in the solution of the equation of motion expressed in terms of the elliptical cylinder coordinates. Applying the orthogonality of the Mathieu function leads to the frequency equations from which one may calculate the eigenvalues of the system. It is shown that letting the natural frequency be zero in the frequency equations derived by the present analytical method yields the buckling conditions. The limiting case of a clamped circular plate is also discussed in detail. Numerical results for all normal modes of vibration and buckling are presented in tables and figures in the cases of elliptaical paltes having six kinds of aspect ratios.

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Currently, the standard testing method of the shear strength of concrete is not yet established. This paper describes the characteristic shear strength of concrete. The characteristics were determined by testing, ordinary cylindrical specimens with two slits on a newly developed mode II type shearing apparatus. Good results and good agreement between the results were obtained. The relationship between the characteristic shear strength and the compressive strength of concrete was clarified in terms of the practical shear strength; moreover, the shear strength the RC beam agreed well with the results of the single-plane shearing test. This new method has proven to be practical for calculating the characteristic shear strength of high strength concrete.

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Since the Great Hanshin-Awaji Earthquake, bridge piers have been undergoing repairs and reinforcement in order to make them more earthquake resistant. This paper investigates the characteristics of steel pipe deformation and the effectiveness of confinement in order to discover the basic design concepts for strengthening a confined column. Two columns were used: a non-loaded, undamaged concrete cylinder and an internally damaged concrete cylinder loaded to just before the ante-peak, that is, just before the compressive maximum strength. These columns were reinforced with steel-pipes and then compressed. Experiments were performed to verify the effects of the physical properties of the fillers injected between the steel pipe and the concrete cylinder on the deformation and rehabilitation of the cylinder and various useful informations were obtained.

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An isolated thin-coated spheroidal short fiber in an infinite body is modeled by a double inclusion which consists of a nested sequence of two inclusions whose elastic constants are different from each other. By adopting the double inclusion method proposed by Hori and Nemat-Nasser to the present model, the volume averages of stresses induced in and around the fiber under the uniaxial external stress are calculated and compared with the exact value obtained by Mikata and Taya. The present value of the average stress in the thin-coat layer is in good agreement with the exact one at the equators of the thin-coat layer. The Mori-Tanaka theorem is extended to the random distribution of the double inclusions in order to analyze the average interaction stress induced in the matrix and the inclusion, and the modified equivalent expression is derived for the double inclusion. By adopting the modified equivalent expression to the thin-coated fiber-reinforced composites, the stresses in and around the fiber are derived as a function of the volume fraction of the thin-coated fiber and the aspect ratio of the fiber. When the volume fraction of the thin-coated fiber is zero, the stress in the thin-coat layer agrees with that in the isolated thin-coated fiber. The stress in the thin-coated layer decreases with increase in the volume fraction of the thin-coated fiber.

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The basic search terms of database usually consist of abstract, title, keynotes, full-text, and so on. However, in the databases of stress analysis before the middle of the 20^th century the search terms would not provide enough information about the subject. The research works in these databases used the difficult mathematical technique and gave few numerical results, because the high performance digital computer did not exist. In order to explain the research results intelligibly to the young reserchers and engineers, we need to supplement the existing database with some mathematics and graphics. In this paper, using the computer algebra system, we propose to create the analytic database with supplementary mathematics and graphics to supplement the important contributions of stress analyses until the middle of the 20^th century. As examples, it is shown that Maunsell's and Isibasi's famous papers concerned with the stress concentration in a notched plate under tension are revived with the supplementary mathematics and graphics. It is important to note that the analytic database with supplementary mathematics and graphics can hand down an important heritage of stress analysis from the 20^th century to the 21^st century as the stress analytical tools.

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The paper presents an axisymmetric solution for the stresses and displaements in an elastic thick plate containing an oblate spheroidal inclusion under circular bending. The interface of the inclusion is assumed perfect bonding. The related spherical cavity and inclusion problems were solved by Tsuchida et al. in 1975 by using Papcovich-Neuber displacement potentials. We extended the method to a spheroidal inclusion problem. Numerical results are given for different values of size, aspect ratio and stiffness ratio. The stress distributions around inclusion are shown graphically.

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This paper considers the axisymmetric contact problem of an elastic half-space indented by a concave or convex rigid punch. Expressing the contact stress under the punch as appropriate series, we reduce the problem to the solution of an infinite system of simultaneous equations. The displacement and stress distributions on the half-space are shown graphically for various magnitude of the contact radius.

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A great deal of studies are recently pursued to mitigate seismic responses of structures through active control arrangements. It may be necessary for response control systems to provide state estimators or structural identifiers when dynamic characteristics are tentatively varied or phisical properties are somewhat uncertain in objective control plants.
The present study is concerned with model reference adaptive control systems to try for the response mitigation of structural constructions having unknown properties, wanting state informations and accepting plural control forces. State variable filters are prepared to compensate for lack of manipulation signals, which are divided into model segments and set in pole assignment way to reduce the increment of auxiliary state variables.
Numerical works are carried out to confirm the validity of the manipulation algorithm and the performance of the control systems under typical quake excitations.

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Using the neural-network-based vibration control suggested by the authors, the control results differ for each learning rate that is to be considered in this paper. A single-degree-of-freedom (SDOF) system structure with a dynamic vibration absorber (DVA) with its damping ratio controlled using neural network algorithm. In actual situation, it is supposed that the neural network algorithm is operated on real time. In the simulation, the control is carried out at the same sampling time of the seismic waves. An optimum-learning rate of the neural network is estimated comparing to the relation between the maximum absolute value of the relative displacements and learning rates. Ten kinds of seismic waves are used as excitation in the simulations.

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We analyzed effects of shapes of snow/ice accretion on conductor given to galloping characteristics of overhead transmission lines by the non-linear time-history analysis making use of the finite element method. This study was made for design of a 500kV trunk line which the Kansai Electric Power Company (KEPCO) plans. Taking four typical accretion shapes for the simulation, we made clear the influences to the galloping generation mode and the maximum vertical displacement by the shapes and initial generation angles of snow/ice accretion.

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In this paper we consider a design method for approximate feedback linearization of single-input/multiple-output nonlinear systems. First, we formulate the problem and then we propose a new approximate linearization method. We adopt a two-step procedure to solve the approximate linearization. First, a coordinate transformation matrix is determines, so that the nonlinear system is transformed approximately into the controllable canonical form representation. Second, a standard nonlinear linearization method is used to transform the controllable canonical form representation into a stable linear system. Application of the proposed method to the Inverted Pendulum demonstrates its effectiveness.

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In this paper, we consider a design method for repetitive control systems with a multi-period repetitive compensator. The repetitive control system is a type of servomechanism for periodic reference signal. The repetitive control system is a neutral type of time delay system and cannot apply for strictly proper plants. Almost all plants are strictly proper. Several modifications of the repetitive control system for strictly proper plants are proposed. It is well known that modified repetitive control is easy to apply for strictly proper plants. Sugimoto and Washida pointed out that the phase angle of the low-pass filter in a repetitive compensator has a bad influence on disturbance attenuation characteristics. They overcame this problem and proposed a design method for repetitive control systems with corrected time delay. However, the method developed by Sugimoto and Washida has improved the disturbance attenuation characteristics only in the low frequency range. Generally, the disturbance includes variable frequency signals. In this paper, we propose a design method for repetitive control systems with multi-period repetitive compensator, in order to attenuate the disturbance with higher frequency range.

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In this paper, we consider a design method for feed-forward controllers for multi-variable systems with non-zero relative degree. Feed-forward controllers play important roles when dynamic character disturbances with the dynamics known are attenuated and an input-output characteristic is specified. Designing feed-forward controllers for multi-variable systems with non-zero relative degree is a difficult problem. The purpose of this paper is to give a state space design method for feed-forward controllers for multi-variable systems with non-zero relative degree.

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With sport equipment, engineering technology has advanced to enable manufacturers to discover and synthesize new materials and new design. There are rackets of all compositions, sizes, weights, shapes and string tensions. At the current stage, very specific designs are targeted to match the physical and technical levels of each user. However, ball and racket impact in tennis is an instantaneous phenomenon creating large deformations of ball/strings and vibrations in the racket. The problem is further complicated by the involvement of humans in the actual strokes. Therefore, there are many unknowns involved in the mechanisms explaining how the specifications and physical properties of the high-tech rackets influence the racket capabilities. The terms used in describing the performance of a tennis racket are still based on the feel of an experienced tester or a player. This paper has investigated the physical properties, predicting the coefficient of restitution, the rebound power coefficient, the post-impact ball velocity and the feel of various high-tech rackets, and estimating the overall racket performances of them using scientific method. It is based on the experimental identification of the racket dynamics and the approximate nonlinear impact analysis with a simple forehand swing model. The predicted results could explain the mechanism of high-tech rackets performance and the difference in performance between the rackets with diffirent physical properties.

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Drag on bluff bodies immersed in a uniform stream is determined by hydrodynamical mechanisms occurring in the near wake behind the bodies. Computer analyses are performed to investigate the relation between the base-shape of the body and the pressure drag on it and find possible drag reduction. Numerical simulations of a uniform flow of a viscous fluid around a bluff body such as a circular cylinder, D-shape or model A and B (modified D-Shapes) have been carried out at the Reynolds number 10⁴ under two-dimensional restriction of the flow field. It is found that the drag on some cylindrical bodies such as the D-shape or model with inward notch is lower than the drag on the corresponding circular cylinder. The lowest drag is found for the model whose back-face is cut with an inward notch and the reduction is found to be 27% on the average.

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The flow around two yawed circular cylinders of the same size inserted into two end-plates is investigated by solving the incompressible Navier-Stokes equations numerically in order to make clear the interaction between two cylinders and the effect of the end-plates on the flow. Two kinds of the flow are examined, i.e. the direction of the flow is parallel and perpendicular to the direction of the inclination of the cylinder. As a typical example, the flow is computed under the following conditions: yaw angle of two cylinders is 30 degree, the Reynolds number is 1000, and the distance between the centers of two yawed circular cylinders is twice as long as the diameter of the cylinders. Moreover, the flow fields of a single yawed cylinder are also investigated and the results are compared to those of the two cylinders.

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We present numerical results of three-dimensional flows around two square cylinders in side-by-side arrangements. The square cylinders in our numerical computations are arranged in various distances between the surfaces of two square cylinders. When the flow around two square cylinders is unsteady, the characteristics of aerodynamic forces acting on the square cylinders depend on the distance between the surfaces of two square cylinders. For examples, it is known from experimental data that values of drag coefficients of two square cylinders in a side-by-side arrangement disagree in the case of short distances between the surfaces of two square cylinders. The computed results at Reynolds numbers 1000 are compared with the experimental results in terms of the aerodynamic characteristics of square cylinders.

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The time evolution of a flow field on a rotating hemisphere bounded by the meridional line is investigated by a numerical model with the two-dimensional incompressible Navier-Stokes equations. We observed a westward propagation of flow patterns, taking a smooth initial condition expressed by streamlines of coaxial circles. The westward flow pattern may be relevant to Stommel's westward intensification on the β-plane.

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Superrotation of more than 100 m s⁻¹ is formed at 60 km in a Venus-like general circulation model (Venus-like GCM) driven by a three-dimensional (3D) heating with a 117-day period. Meridional circulation efficiently pumps up angular momentum from the surface to the cloud-top level (65-70km) as expected from the Gierasch mechanism. Thermally-forced or enhanced waves with zonal wavenumbers of 1 and 2 produce equatorward eddy momentum fluxes, being possible candidates for the equatorward momentum flux caused by large horizontal diffusion in the Gierasch mechanism.

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Numerical simulations of two-dimensional flows around a cross-flow type wind turbine are investigated. The turbine studied in this paper has cylindrical shape with 12 small blades along its periphery. The governing equations are the incompressible Navier-Stokes equations. A rotating coordinate system, which rotates at the same speed of the turbine, is used in order to simplify the boundary conditions on the blades of the turbine. Additionally, a boundary fitted coordinate system is employed in order to express the shape of the blades precisely. The fractional step mathod is used for solving basic equations. The third order upwind scheme is employed for the approximation of non-linear terms. A cross-flow wind turbine equipped with a guide vane to enhance its performance is examined as well. The presence of the vane results in a power increase of about 1.5.

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The formation of an axisymmetric liquid jet when one Newtonian liquid is injected through an orifice into another immiscible Newtonian liquid, and its breakup into drops, is studied using direct numerical simulations. A front tracking/finite difference method is used to track unsteady motion of the liquid-liquid interface. Various combinations of the non-dimensional numbers are examined (Re=80, 160, and 320; We=5 and 8; Fr=4, 8, 32, and ∞ ) for constant ratios of density (ρ_c⁄ρ_j=1.25) and viscosity (μ_c⁄μ_j=1), where subscrips c and j denote continuous phase and jet, respectively. For all cases examined, the droplets break off due to capillary wave instability. Double-node breakup where two most-unstable waves become one drop, is often observed, because the vortical motions in the external fluid affect the breakup process unlike the breakup of a liquid jet in air. This is one of the reasons that a distribution of drop sizes is produced by the breakup and the averaged size of droplets differs from that predicted by linear stability theory.

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It is possible thermal expansion from heat generation by slicing deforms a single-crystal silicon ingot but the authors can find no report on the point. In addition, numerical analysis is useful to clarify the mechanism of wafer warping but no paper has been reported the numerical analysis from the start to end of the wafer slicing process. The authors carried out experiments for the wafer slicing. In addition, a finite element analysis was carried out in order to solve the warping mechanism from the start to end of the wafer slicing process. The warp of wafer in the vertical direction was 6.05 μ m in the experiment whereas the warp in the finite element analysis was 6.96 μ m. The result by the finite element analysis gave good agreement with experimental one. This paper suggests that thermal expansion of the ingot has great influence on the warp of wafer. As ingot length is increased, the warp of wafer on the side end of ingot was also increased but the warp of wafer on the same distance from center in the axial direction of the ingot was decreased. It suggests that stiffness of the wafer is increased as ingot length is increased.

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The present paper deals with a transient plane thermoelastic problem of a piezoceramic circular plate exhibiting crystal class 6mm symmetry. It is assumed that the plate is initially at the uniform temperature and suddenly subjected to an axisymmetric heating temperature on both surfaces. The temprerature rise in the plate is obtained by solving the three-dimensional heat conduction equation. The elastic and electric fields are analyzed by applying a plane-stress formulation based upon thermoelastic displacement and piezoelectric potential functions. Numerical results for the transient stresses and electric potential in a cadmium selenide plate are compared with those derived from a three-dimensional formulation. Finally, the errors resulting from the plane-stress approximation are investigated.

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The method of an analytical development of isothermal elastic and thermoelastic problems for a medium with inhomogeneous material properties is developed. For such inhomogeneous medium, an analytical method of development for the polar cylindrical coordinate system has already been proposed by M. K. Kassir under the assumption that the shear modulus of elasticity G is changed arbitrarily with the power product form of the variable z. However, the fundamental equation system proposed is not sufficient to solve the boundary value problems. In this article, introducing the two kinds of displacement functions, the analytical method of development for the plane isothermal and thermo elastic problems is established. As illustrative examples, the isothermal plane elastic problems of a semi-infinite medium and a slab are treated. Numerical calculations are carried out for several cases taking into account the variety of shear modulus elasticity G . Numerical results are shown graphically.

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Nonlinear dynamics of complex chemical processes in an open system was investigated by employing the Brusselator model for a theoretical approach and emulsion polymerization of vinyl acetate for an experimental approach. Dynamic instabilities of chemical oscillations observed in both the continuous flow systems were discussed from a viewpoint of design methodology of chemical process systems and operation.

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The purpose of the present work is to propose a new design method of mixing field by means of an emergent synthetic approach and to discuss applicability of this method to a two-dimensional laminar mixing field. The presented method consists of the following steps: 1) A very simple flow motion is assigned for a basic component. 2) A chaotic mixing field is produced by spatially arranging a few components. 3) The chaotic mixing field is estimated by the method based on the information entropy theory. 4) A group of suitable configurations of components for mixing is selected by a genetic algorithm. 5) Through the evolutional steps by iterating 2) – 4), the configuration of components finally reaches to the very near optimal one. A simple flow system consisting of two and/or three parallel rotating cylinders was tested. The results obtained by this method were very close to the optimal configuration of cylinders for obtaining a well-mixing state.

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We propose a hybrid modeling method to carry out numerical simulation of dynamic process behavior in a chemical reactor, which can satisfy both purposes of lightening a load of a process designer and of simulating the process more accurately. In this work, the hybrid model consists of an ordinary differential equation model and a partial differential equation model, and is applied to dynamic simulations of starting up a polymerization reactor. Then, in order to carry out the hybrid model simulation accurately and efficiently, it is necessary to make a simulation system in which two different simulators can work cooperatively. As a consequence of the dynamic process simulations, the hybrid model simulation is found to be useful when appropriate models are selected by considering whether the spatial heterogeneity caused by flow condition affects dynamic behavior of the whole process or not.

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We consider the (linear) elastic wave equation and construct asymptotic solutions. At first, we summarize the procedures of the construction, and next give the concrete forms (asymptotic solutions) of the waves reflected by boundaries in various situations, i.e., in the cases where a discontinuous wave like the delta function is reflected by the boundary, where a wave is reflected by a hole empty or full of some liquid, etc. And we try to get information of the situations from the reflected waves.

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Reflection of an obliquely incident internal solitary wave by a vertical wall in stratified fluids is studied numerically. The results are compared with the prediction by Miles that is valid for small-amplitude wave. We derive the following three main conclusions: (i) The effect of finite amplitude tends to prevent the Mach reflection to occur. (ii) The deviation from the prediction by Miles is larger than that of the water waves with the same incident-wave amplitude. (iii) When the amplitude of incident solitary wave is large, radiation wave is observed behind the usual reflected wave. The physical mechanism of these conclusions is also presented.

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A sizing optimization procedure for fluid-structure interaction problems is presented. The proposed procedure consists of two phases. In the first phase, the design variables are updated so as to satisfy constraint conditions. In the second phase, the design variables are updated according to a linear approximation of the constraint condition so as to gradually decrease the total weight of structure. The total weight of the structure always and gradually decreases, and structural deformation also proceeds gradually, effectively avoiding sudden change in deformed shape of the structure. This process eliminates the possibility of severe and unnecessary distortion of fluid meshes, and reduces the need for re-meshing. A numerical example is presented demonstrating the validity of the proposed optimization method.

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Some applications of Convex-Subspace Single Linkage Method (CSSL method) to a multi-peaked structural optimization problem are described. CSSL method is one of global optimization methods, which use a gradient component of an objective function. This method has two main processes. One is a local optimizing process and the other is a clustering process. In this paper, one mathematical example and two examples of a structural optimization are illustrated. Solving the mathematical example, a validity and effectiveness of the method is investigated. As structural optimization problems, a layout design problem and a fiber orientation design problem are solved. The layout design problem is to optimize a location of inserted reinforcement for a beam structure. THe fiber orientation design problem is to optimize a fiber orientation of a laminated composite plate for an eigenfrequency problem. All of these are a global optimization problem. Especially, for the fiber orientation design problem, optimization using CSSL method and NN approximation is attempted, and a practicality of the method is investigated.

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This paper proposes a method for damage identification of cable net structures for space application using the numerical simulation by genetic algorithm. In the algorithm the disconnected position of cables (expressed by binary code) is identified based upon shape errors of the surface (evaluated as fitness). Unlike the usual methods such as sensitivity analysis or neural network, the proposed method has basic capability for identification of cable net structures with uncertain number of damages. As a result of numerical simulations based on the proposed algorithm, it is recognized that identification of the plural damages is basically available and effective for the cable net structures such as large space antennas.

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We propose a numerical method to solve a two-phase flow with mass transfer through its mobile interface. Numerical simulations of axisymmetric liquid-liquid jets with mass transfer are carried out using a level set method. The dispersed and continuous phases and a solid nozzle are calculated together in the overall computational domain as solutions of the governing equations of fluids. In the model of mass transfer we assume that the mass concentration of the dispersed phase is constantly saturated, so that uni-directional mass transfer at the two-phase interface is considered. The shrinkage of the dispersed phase due to the dissolution is taken into consideration in the present level set formulation.

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Flow with snowfall past a snow fence is computed numerically and the generation of the snowdrift is investigated. The numerical method employed in this study can be divided into following four parts: (1) Calculation of the air flow around the snow fence by using fractional step method with a generalized coordinate system; (2) Calculation of the movement of test particles which represent snowfall to predict snow accumulation; (3) Estimation of the snow transfer on the ground due to wind through friction; (4) Determination of the shape of the snow surface. These computational procedures are repeated in every time step since the shape of the region is changed by the procedure (4). It is procedure (2) that is newly developed in this study. The results are compared with the field observation and the agreement is satisfactory.

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In recent years, several useful calculation methods for turbulent shear flows have been reported. The author proposed the harmonic mixing length model that originates from the ordinary mixing length model, and showed analytical results for several kinds of turbulent flows: circular pipe flow, parallel plate flow, Couette flow, open-channel flow, in volumes 47, 48 of Theoretical and Applied Mechanics. The proposed concept also seems to have generality and applicability to other types of uniform-property flows. This paper shows a useful calculation method to analyze shear flows in straight ducts of uniform cross-section. The method is then, using harmonic mixing length, applied to calculations of turbulent shear flows in rectangular sectioned channel, including the ones in square sectioned channel and the ones between two infinite parallel plates. The concept of harmonic mixing length is commonly useful both in the calculation of axial velocity and in that of secondary flow.

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Chaotic dynamics of drops falling from a nozzle was studied both numerically and experimentally. We demonstrate the low-dimensionality of the chaotic attractor by analyzing the drop shapes captured by a high-speed camera. The dynamics of the falling drops was well described by a one-dimensional map in a wide range of flow rates. It will be illustrated that the geometry of the chaotic attractor is well understood by considering a potential surface as a function of mass and position of the center of mass.

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We precisely discuss the choice of a parameter in regularization schemes for ill-posed problems under a multiple-precision arithmetic environment. A regularization scheme gives a mathematically well-posed equation in a suitable space, however, its discretizations become ill-conditioned for small regularization parameters, and precise numerical computation seems impossible in the double precision computing environment.
To overcome the difficulty, we have proposed an effective use of multiple-precision arithmetic in order to obtain reliable numerical results for ill-conditioned problems. In the present research, we show that a priori information about solutions is essentially required for the choice of an appropriate regularization parameter, when a discretized Tikhonov regularization scheme is carried out in the multiple-precision arithmetic environment.

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We are given in an area the volumetric discharge strength ƒ(x) from an aquifer and hydraulic heads h^(j) in wells for j = 1, 2, …, m at m interior observation points x^(j) in the area. Our problem consists of identifying the transmissivity θ(x) of the aquifer. The original identification problem is formulated as a variational problem for unknown transmissivity, which leads the variational problem to a system of primary and the adjoint problems in the form of conventional boundary value problem of the steady seepage equation. With an initial guess of the transmissivity distribution, an iterative process of identification starts in order to attain the convergent transmissivity by numerically solving the boundary value problems using the finite element method. The method is tested for simple examples, showing its potential applicability in field practice.

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In this paper, we consider an inverse scattering problem for multiple obstacles D = ∪^N_j=1D_j ⊂ R³ with different types of boundary condition for D_j· By constructing an indicator function from their scattered wave field, the number N and the location of each obstacle, as well as the type of boundary for each obstacle can be recovered.

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Effectiveness of the A – Ø method is considered. Convergence of Bi-Conjugate Gradient method (BiCG) is faster with the electric scalar potential than without it. Also, convergence of BiCG changes according to boundary conditions of the potential. The TEAM model and a transformer model are considered as numerical examples.

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