The finite-difference time-domain (FDTD) method is useful in solving three-dimensional (3D) electromagnetic problems. However, it contains a numerical instability because it is a complete explicit method, and huge amounts of memory are required in the case of 3D analysis. The implicit FDTD method called the Alternating Implicit Block Overlapped (AIBO)-FDTD method was proposed for two-dimensional (2D) electromagnetic analysis. In our study, the 3D AIBO-FDTD method is developed by the modification of the 2D method. This method is suitable for parallel processing since the computational domain can be effectively partitioned. This property is especially compatible with implementations using distributed-memory multiprocessor systems such as PC clusters, which provide a huge memory space that accommodates a large problem. Although this method seems numerically stable since the implicit scheme is included, our result shows that the numerical instability occurs when the time step exceeds Courant's stability condition. This condition is still more relaxed than the conventional FDTD method. Furthermore, we demonstrated that parallel processing is an effective technique for improving the performance of the 3D AIBO-FDTD method, while this method is slower than FDTD when it is run on one processor.

We discuss numerical interpolation schemes used in Vlasov codes. An improved conservative semi-Lagrangian scheme is compared with the latest non-conservative and conservative schemes for a long run-time nonlinear problem of the beam–plasma interaction with respect to the mass and energy conservation.

A numerical code has been developed for analyzing the time evolution of the shielding current density in the high-temperature superconductor (HTS) bulk. In the code, the shielding current equations are discretized by means of the element-free Galerkin method and the resulting nonlinear system is solved by use of the pseudo Newton method with a variable relaxation factor. By means of the code, the shielding current density is calculated in cases where the ac current flows in a coil placed just above the HTS. The voltage induced in the coil is evaluated as a function of time and its spectral analysis is performed. The results of computations show a qualitative agreement with Mawatari's experimental results.

One of the most practical objectives for the use of virtual reality (VR) systems in science is facilitating an intuitive understanding of complex physical phenomena. We developed a VR system, called CompleXcope, which can represent a ‘real’ three-dimensional visual and aural environment. However, communication with other researchers at a remote site (VR space) regarding simulation results is difficult, since this system is very large and is not portable. Therefore, it is important to construct a multilateral communication network system, in which researchers at any remote site are equally able to observe simulation results from any point and take initiative in controlling the display of the image in a virtual environment (VE), and in which the control is simultaneously transmitted to all of the remote sites. In the present paper, we describe a collaborative virtual environment and an example in which the simulation results are applied.

The CAVE-type virtual reality (VR) system was introduced for scientific visualization of large-scale data in the plasma simulation community about a decade ago. Since then, we have been developing a VR visualization software, VFIVE, for general CAVE systems. Recently, we have integrated an open-source visualization library, the Visualization Toolkit (VTK), into VFIVE. Various visualization methods of VTK can be incorporated and used interactively in VFIVE.

The boundary element method (BEM) has been so far applied to various engineering fields as the discretization method. The BEM, however, has an inherent demerit. The accuracy of the inner-point formula is drastically degraded in the vicinity of the boundary. In order to resolve the above difficulties, the regularization technique has been so far applied to the inner-point formula. In the present paper, the novel approaches are developed for enhancing the accuracy of the inner-point formula in the vicinity of the boundary and their performances are investigated quantitatively by applying it to a three-dimensional problem. In order to obtain the high-accuracy solution in the vicinity of the boundary, two approaches have been proposed in the present study: the high-accuracy regularization and the virtual-region method. The former is a natural extension of the regularization technique, whereas the latter originates from a widely different idea. In the latter, the solution is evaluated through the following procedures: the boundary integral equation is solved on the boundary of the virtual region in which the original region is contained and, subsequently, the solution is evaluated by means of the inner-point formula over the virtual boundary. The results of computations show that the accuracy degradation of the inner-point formula is avoided by means of both the proposed methods. In addition, the accuracies of the proposed methods are higher than that of the regularized inner-point formula. From the above results, we can conclude that the proposed methods, the high-accuracy regularization and the virtual-region method, are suitable for improving the accuracy of the numerical solution of the BEM.

Plasma particle simulations are performed using GRAPE-6, a special-purpose computer for calculating gravitational N-body systems. GRAPE-6 rapidly calculates the gravitational force between particles using specialized pipeline processors. The peak performance of a unit of GRAPE-6 reaches 985 GFLOPS. We investigated speeding up plasma simulations through the use of GRAPE-6 for the calculation of Coulomb interactions, which have the same form of central force as the gravitational force. As an example of plasma particle simulation using GRAPE-6, we simulated the Buneman instability. As another example of plasma particle simulation, we simulated a Coulomb crystal in a dusty plasma. The formation of a Coulomb crystal was observed under typical laboratory conditions. We found that GRAPE-6 can perform the entire operation of the simulation of a Coulomb crystal with 5 × 103 particles up to 210 times faster than a 1.6-GHz Pentium4 CPU.

In this paper, we present a scheme for analyzing structures which have complex shape models. The targets of the structural analysis usually consist of a combination of simple shape models generated using modeling tools such as CAD systems. On the other hand, in the field of computer graphics, there have been proposed a number of techniques that make it possible to create complex shape models from point clouds obtained by three-dimensional (3D) range scanners. One suitable representation for the reconstructed shape is an implicit surface model. One typical advantage of the implicit representation is fast inside/outside distinction. For the analysis of a structure represented as an implicit surface model, we use the Element-Free Galerkin Method (EFGM), which is suitable for the analysis of a structure with an implicit surface representation. For the analysis with the EFGM, internal nodes spread in the object are required and the nodes can be generated easily using the property of fast inside/outside distinction. We also note that the EFGM does not require any information about connectivity between adjoining nodes inside the model. We also present some numerical results of 3D stress problems.

OpenMP is a directive-oriented paradigm for parallel programming applicable to shared memory parallel computers. On the other hand, High Performance Fortron (HPF) is also a directive-oriented paradigm but for distributed memory machines. Thus, it could be very interesting to compare their programming applicability and parallel performances. We have converted four SPEC OMP 2001 benchmark programs, which are written with OpenMP and designed to evaluate the performance of shared memory parallel computers, into HPF, and evaluated parallel performances. We also point out problems that we had faced during conversion, and discuss solutions for them. Finally, we have improved the HPF performance by modifying the original source code. We could get good performance with HPF quite similar to OpenMP with SWIM, and moderate performance with APSI.

It is shown that the exact nonlinear solution for the Hall–Alfvén waves can be obtained in a uniformly rotating weakly ionized plasma such as those which exist in various types of accretion disks. In addition this piece of work demonstrates a method of eliminating the inaccuracies embedded in the literature on this subject.

Direct numerical simulation of fully three-dimensional, compressible and nonlinear magnetohydrodynamic equations in the Large Helical Device is carried out in combination with the passive particle simulation. In the simulation, strong vortical motions are excited by the pressure-driven instability and form the mushroom-like structures of pressure. It is shown by the passive particles analysis that the fluid volumes around the resonant magnetic surfaces experience finite compressibility and toroidal deformation, which are both excited by the strong vortical motions. The passive particles simulation helps us to investigate local structures even for low Fourier wavenumber modes.

The nonlinear three-dimensional magnetohydrodynamics (MHD) code NFTC and the basic algorithms included in the code are presented. NFTC code is used for simulations of nonlinear neoclassical instabilities (or neoclassical tearing modes (NTMs)) in tokamaks. An effective fully implicit numerical scheme allows the transport profile to evolve self-consistently with the nonlinear MHD instabilities and externally applied sources and sinks. It is shown that numerical code has enough accuracy for simulation of plasma instabilities in arbitrary three-dimensional geometry. The coefficients of a special finite-difference scheme in the radial direction are constructed in the form which gives the exact asymptotic dependence of the solution by the ratio of small parameters near high derivatives and the mesh step size. The reproduction of the nonlinear threshold effects for NTMs in conditions of anisotropic heat conductivity is presented.

We used Monte Carlo simulation code DEGAS and studied the neutral particle behavior in the Compact Helical System (CHS) three-dimensionally. In contrast to other helical devices, the CHS plasma in the standard configuration has contact with the inner vacuum vessel wall like the material limiter used in many Tokamaks and the neutral recycling becomes dominant there. As the intensity of neutral recycling changes also along toroidal direction, we extended our previous simulation model geometry three-dimensionally and compared the results of these models. We found the variation of the gap between the vacuum wall and main plasma enhanced toroidal transport of hydrogen molecules and atoms. As the formation of the edge transport barrier (EBT) discovered recently in CHS is characterized by a clear drop in Hα emissions, it is interesting to study the relationship with the profile of atomic/molecular hydrogen and the Hα emission profile. We estimated emission not only from excited hydrogen atoms but also from dissociated molecules with a collisional radiation model. We found that our Hα detector signal in CHS mostly came from excited atoms and that the emission profile largely changed with the ETB formation.

A three-dimensional model for the numerical simulation of transport in the edge plasma of modern fusion devices is developed. The model is based on the Braginskii set of equations which are solved with the help of a Monte Carlo method by three-dimensional plasma transport code E3D. The multiple coordinate system approach and interpolated cell mapping technique used in E3D allow us to avoid artificial numerical cross-field transport due to a high anisotropy of Braginskii equations in the case of general magnetic configurations including ergodic regions. The complete self-consistent set of fluid equations (equations for the density, parallel momentum, ion and electron temperatures) has been successfully implemented in E3D. A stabilization method for iterating coupled momentum and density equations is discussed.

Three-dimensional hybrid simulation of a plasma current-carrying column reveal two different regimes of sausage and kink instability development. In the first regime, with small Hall parameter, development of instabilities leads to the appearance of large-scale axial perturbations and eventually to bending of the plasma column. In the second regime, with a four-times-larger Hall parameter, small-scale perturbations dominate and no bending of the plasma column is observed. Simulation results are compared with laser probing experimental data obtained during wire array implosions on the Zebra pulse power generator at the Nevada Terawatt Facility.

A multi-scale nonlinear magnetohydrodynamic (MHD) evolution scheme is developed for the numerical analysis of a heliotron plasma as beta increases. In this scheme, the fast time scale dynamics is given by the nonlinear MHD code based on the reduced MHD equations and the slow dynamics is carried out with three-dimensional static equilibrium code. The time evolution is calculated iteratively with a linear interpolation technique for the equilibrium quantities. This scheme is applied to the analysis of the Large Helical Device plasma. Self-organization of the pressure profile induced by the interchange mode is obtained.

A three-dimensional neutral transport model using the DEGAS version 63 Monte Carlo code is described in order to understand the behavior of neutrals in the non-axisymmetric anchor region of the GAMMA 10 tandem mirror. A precise mesh structure with three-dimensional geometry was built up and the simulation was carried out under a plausible assumption of the particle source on the basis of experimental data. In standard ion-cyclotron-range-of-frequency heated plasmas, detailed measurements of Hα line emission were performed using a 5-ch Hα detector array in the outer-transition region of the east anchor cell and the experimental results were compared with the simulation. The spatial profile of Hα emission predicted from the simulation agreed well with the experimental result and the distinctive behavior of neutrals in this region was clarified.

Stability analysis of external magnetohydrodynamic modes is carried out to investigate an effect of the aspect ratio on the achievable plasma pressure. The decrement of the aspect ratio improves the achievable plasma pressure and increases the toroidal mode number of the external mode restricting the pressure.

A newly developed numerical model calculating the distribution and damping of radiofrequency fields by sloshing ions is presented. The model solves time-harmonic Maxwell's equations written in terms of the electric field. It uses a two-dimensional grid and a Fourier series in the third coordinate and is based on a non-staggered mesh not aligned along the steady magnetic field. The numerical stability of the scheme is discussed, and the convergence analysis is presented.

A fusion plasma is modeled by a one-dimensional Vlasov–Maxwell system of equations. Particle annihilation is considered by a dedicated factor in the Vlasov equation. A term describing background damping mechanisms is considered in the equation relating the electric field to the current (Berk–Breizman model). Results are presented for simulations in a one-dimensional velocity space, the extension by a further velocity dimension is sketched. As an initial condition, a bump-on-tail distribution is assumed. The time evolution of the system is studied and characterized with respect to different points in parameter space. A fractional steps method using cubic splines interpolation is applied for time-integrating this system.