Relative to single-band models, multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials. In this brief review we discuss the physics of three multiband models (the three-band Hubbard, the periodic Anderson, and the Falicov-Kimball models) that was obtained by numerical simulations at zero temperature. We first give heuristic descriptions of the three principal numerical methods (the Lanczos, the density matrix renormalization group, and the constrained-path Monte Carlo methods). We then present generalized versions of the models and discuss the measurables most often associated with them. Finally, we summarize the results of their ground state numerical studies. While each model was developed to study specific phenomena, unexpected phenomena, usually of a subtle quantum mechanical nature, are often exhibited. Just as often, the predictions of the numerical simulations differ from those of mean-field theories.

This paper opens a series of papers aimed at finalizing the development of the lattice Boltzmann method for complex hydrodynamic systems. The lattice Boltzmann method is introduced at the elementary level of the linear advection equation. Details are provided on lifting the target macroscopic equations to a kinetic equation, and, after that, to the fully discrete lattice Boltzmann scheme. The over-relaxation method is put forward as a cornerstone of the second-order temporal discretization, and its enhancement with the use of the entropy estimate is explained in detail. A new asymptotic expansion of the entropy estimate is derived, and implemented in the sample code. It is shown that the lattice Boltzmann method provides a computationally efficient way of numerically solving the advection equation with a controlled amount of numerical dissipation, while retaining positivity.

This paper is concerned with the adaptive grid method for computations of the Euler equations in fluid dynamics. The new feature of the present moving mesh algorithm is the use of a dimensional-splitting type monitor function, which is to increase grid concentration in regions containing shock waves and contact discontinuities or their interactions. Several two–dimensional flow problems are computed to demonstrate the effectiveness of the present adaptive grid algorithm.

Computational simulation of the radiating structure of a microwave from a pyramidal horn has been successfully accomplished. This simulation capability is developed for plasma diagnostics based on a combination of three-dimensional Maxwell equations in the time domain and the generalized Ohm's law. The transverse electrical electromagnetic wave of the TE_1,0 mode propagating through a plasma medium and transmitting from antenna is simulated by solving these governing equations. Numerical results were obtained for a range of plasma transport properties including electrical conductivity, permittivity, and plasma frequency. As a guided microwave passing through plasma of finite thickness, the reflections at the media interfaces exhibit substantial distortion of the electromagnetic field within the thin sheet. In radiating simulation, the edge diffraction at the antenna aperture is consistently captured by numerical solutions and reveals significant perturbation to the emitting microwave. The numerical solution reaffirms the observation that the depth of the plasma is a critical parameter for diagnostics measurement.

Two algorithms for dwell time adjustment are evaluated under the same polishing conditions that involve tool and work distributions. Both methods are based on Preston's hypothesis. The first method is a convolution algorithm based on the Fast Fourier Transform. The second is an iterative method based on a constraint problem, extended from a one-dimensional formulation to address a two-dimensional problem. Both methods are investigated for their computational cost, accuracy, and polishing shapes. The convolution method has high accuracy and high speed. The constraint problem on the other hand is slow even when it requires larger memory and thus is more costly. However, unlike the other case a negative region in the polishing shape is not predicted here. Furthermore, new techniques are devised by combining the two methods.

A novel method for the generation of unstructured triangular surface meshes is presented. The method is based on remeshing techniques including edge splitting/contraction and edge swapping. Normalized edge lengths, based on a metric derived from curvature or from a user–specified spacing, are employed as the remeshing criterion. It is assumed that the geometry is input in the form of composite parametric surfaces, with Ferguson or Nurbs type multiple patch representation. Examples involving typical aircraft geometries and a ship model, are included to demonstrate how high quality meshes can be efficiently generated on surfaces with a high degree of geometric complexity.

The comparable feature analysis of NAMD and GROMACS molecular dynamics packages has been done. The benchmarks of 72 and 128 Dipalmitoylphosphatidylcholine (DPPC)/water have been constructed using a cluster (3GHz-Xeon processors and Myrinet network) and the comparison has been performed using GROMOS87 and CHARMM27 force fields modified for lipids with GROMACS and NAMD software packages, respectively. The GROMACS has been displayed as faster than NAMD, likely due to united-atom character of GROMACS and good implementation features. The GROMACS reaches saturation and goes to the worst results, the reason of which is that the program spends more time on communications between processors.

In this paper, we present a new fourth-order upwinding embedded boundary method (UEBM) over Cartesian grids, originally proposed in the Journal of Computational Physics [190 (2003), pp. 159-183.] as a second-order method for treating material interfaces for Maxwell's equations. In addition to the idea of the UEBM to evolve solutions at interfaces, we utilize the ghost fluid method to construct finite difference approximation of spatial derivatives at Cartesian grid points near the material interfaces. As a result, Runge-Kutta type time discretization can be used for the semidiscretized system to yield an overall fourth-order method, in contrast to the original second-order UEBM based on a Lax-Wendroff type difference. The final scheme allows time step sizes independent of the interface locations. Numerical examples are given to demonstrate the fourth-order accuracy as well as the stability of the method. We tested the scheme for several wave problems with various material interface locations, including electromagnetic scattering of a plane wave incident on a planar boundary and a two-dimensional electromagnetic application with an interface parallel to the y-axis.