Box set subtraction is widely used in SAMR to compute data dependency and nested restriction. Traditional box set subtraction algorithms suffer from high time complexity, which often dominates execution time for large scale SAMR simulations. In this paper, a divide and conquer box set subtraction algorithm with linear time complexity was proposed, and enhanced by domain decomposition parallelization. Experiment results on regular box set and irregular box set of SAMR application verify linear time complexity property. And for large scale problems, our algorithm shows great improvement on computing time.

Dynamics of cubic-quintic nonlinear Schrödingeröequation are studied numerically with symplectic method. Behaviors of the equation are discussed with increased quintic nonlinear parameter. We observe homoclinic orbit crossing and elliptic orbit in turn and the system has recurrent solutions. Pattern drifting of solutions is also discussed. It is shown that pattern drifting can be slowed down by increasing the quintic nonlinear parameter.

A mathematical model is developed to analyze numerically coal pyrolysis and heat transfer inside a heated coal particle.Endothermic effect of decomposition and transpirational convective heat transfer are taken into account.A coupled comprehensive model was validated with experimental data of pulverized coal and large particles.Then,temperature history and coal pyrolysis of coal particle heated were analyzed numerically.Effects of endothermic of pyrolysis,transpirational convection,volatile content and particle size were investigated to understand physically transient temperature and volatile evolution of coal particle.

In order to investigate interface structure of composite films,several solid solution structures and elastic properties of a single atom in transition metal nitrides are studied with first principle method based on density functional theory.The calculation shows interesting results:(1) A silicon atom could not form a solid solution in TiN,ZrN,HfN,or TaN crystallites.It is the same for a germanium atom in TiN crystallite.(2) As distance between crystallites becomes large,a silicon atom in TiN,ZrN,HfN and TaN or a germanium atom in TiN may form interstitial or substitution interface structures.(3) A silicon atom in NbN or a boron atom in TiN could form interstitial or substitution interface structures.(4) Interface structures of a silicon atom in VN or a carbon atom in TiN is a substitution structure.Studies of mechanic properties indicate that modulus of elastic,bulk,shear and Young's of lower energy substitution and interstitial solid solution is less than that of transition metal nitrides.

A parallel software module of FMM (fast multipole method) for three-dimensional Laplace kernel functions, JASMIN-3DLapFMM, is designed and implemented. The module is based on two phases parallel strategy of both processes and threads. A parallel software module is successfully used to solve the far field potential of electrostatic fields. With a fixed problem size of single processor,almost linear weak parallel scalability is obtained for a grand scale problem with 10¹⁰ particles on more than ten thousand processors. With a fixed size of total problem and 1024 processors, about three times speedup is obtained on four threads.

A non-isothermal three-dimensional(3 D) two-phase flow transport model is developed for a proton exchange membrane fuel cell(PEM FC) with straight flow channels.Based on characteristics of water transport between membrane and gas phase,a non-equilibrium model is developed for liquid water transport in membrane,considering electroosmosis,concentration diffusion and electrochemical reaction.A finite volume method is used to discretize governing equations and solution code is developed.The model is used to simulate multi-physical field coupled transport in a PEMFC.Investigations are performed for water vapor concentration,liquid water saturation,membrane water content distribution and liquid water transport velocity.Temperature field inside a cell and predicted polarization are obtained.

Communication algorithms need to exchange data between adjacent subdomains. The detection of adjacent subdomains is an import task for communication algorithms, which can be done by solving an intersection problem of boxes. An interval tree algorithm is proposed for intersection problems. Taking advantage of structured mesh applications, it is able to maintain 0 (Nlog N) time complexity. Numerical experiments show that the algorithm is able to achieve high computational efficiency and good scalability. It supports parallel computing of miUion-box scale.

An improved shooting method is applied to 1D Gross-Pitaevskii equation,which describes Bose-Einstein condensate of neutral atoms in harmonic trapping potential at zero temperature.Eigenvalues of ground state of condensates with different nonlinear coefficient are given.Interference of three condensates after removing the trapping potential is studied with symplectie method.A periodic evolution is shown.Influence of relative phase on interference of condensates is discussed.

Symplectic method is applied to solve numerically 1D time-dependent Gross-Pitaevskii equation. "Breathing" of the condensate is numerically illustrated. Interaction of two Bose-Einstein condensates is investigated as external potential is zero at t=0. Interference between two condensates is observed. Evolution of density due to interference at various relative phases is studied.

Interaction of multi-atom molecular ions with intense laser pulse is studied. High-order harmonic generation plateau is extended and conversion efficiency is enhanced.Physical mechanism of plateau extension is explained with classical theory.

A one-dimensional load balancing method is proposed with memory constraint.It is an iterative method which converges to optimal partitioning linearly.Experiments on(1 024) CPUs with typical load imbalance models and a three-dimensional molecular dynamics program show effectiveness of the method.

Dynamics of one-dimensional hydrogen molecule in two-color intense laser field is studied with classical theory and symplectic algorithm.Classical trajectories are obtained by solving Hamiltonian equations numerically. Probabilities of H₂⁺,H₂²⁺,H,H⁺ are evaluated.Classical dynamics caused by laser intensity,frequency,and phase are illustrated and explained.

Navier-Stokes equations are solved numerically to simulate vortex motion in separated flows using detached-eddy simulation (DES) method in Saplart-Allmaras one equation model. A finite volume scheme is employed. Spatial discretization is performed with Jameson central scheme. Time integration is implemented by a dual time-stepping approach. Vortex structures of flow over a circular cylinder or a stall airfoil simulated agree well with physical analyses and experimental data.

Evolution of front with speed dependent on curvature is considered. The speed includes both normal and tangent components. Change of total variation of propagating front depends only on derivative of normal speed about curvature where curvature is zero. The tangent speed has no influence on change of total variation.

Classical trajectory method is used in 1D and 3D models to study classical dynamics of Hydrogen molecular ion (H₂⁺) in intense laser fields. Probabilities of survival, ionization, dissociation and Coulomb explosion and average distance between electron and the mass-center are calculated. It is shown that the 1D model is available for dynamics of hydrogen molecular ion in intense laser fields.

A numerical method applicable to unstructured mesh is proposed to compute 3D hypersonic ionized and radiating flowfields in thermo-chemical nonequilibrium. The flowfield is described with multi-specy N-S equations. The chemical model includes 11 species(O₂, N₂, O,N, NO, NO⁺, N⁺, O+, N₂⁺, O₂⁺, e^-) and 20 reactions. For thermal nonequilibrium effect, a two temperature model is considered. Radiation transfer equation (RTE) is solved with finite volume method. Numerical result on MUSES-C is shown and compared with referenced data. Influence of radiation on flowfield is discussed.

An improved finite difference method in solving vector wave equations based on H fields for full-vectorial analysis of optical waveguides is described.A six-point finite difference scheme of high accuracy is constructed to approximate cross-coupling terms.It takes into account the discontinuities in derivatives of magnetic component at horizontal and vertical interfaces.Moreover,the scheme is independent of structure of waveguide due to explicit expressions.The guided-mode patterns and normalized propagation constants of a step-index fiber,a rectangular waveguide and a rib waveguide are presented.The hybrid nature of full-vectorial guided-modes is demonstrated.The results agree well with analytical solutions and the benchmark results of modal transverse resonance method.It demonstrates accuracy and convergence of the method.

The control of period-doubling bifurcations and chaotic attractor periodic orbits in a discrete nonlinear dynamical system is realized by translation.Appropriately adjusting the translation parameter and system place,any periodical orbit can be reached in a chaotic system.This method is applied successfully to the Logistic map and the Henon map.

A classical trajectory method is used to study a diatomic molecule(HF) interacting with chirped intense laser pulses.In the model,the motion of nuclei is described with classical Hamiltonian canonical equations.The Hamiltonian equation is solved numerically by a symplectic method,and the initial conditions are chosen by a single trajectory in the field-free case at random.The classical dissociation of HF by chirped pulses is evaluated.The dissociation probabilities with different laser intensities are discussed.Dissociation probabilities at different initial states are also investigated.The dissociation process is illustrated by classical phase trajectories and energy versus nuclei separation.

The ground state wavefunctions of dilute Bose-condensed atoms in a harmonic trap at T=0 are evaluated by a symplectic shooting method.Stability of the wavefunctions is tested,and a stable wavefunction is used as the initial input of the time-dependent Gross-Pitaevskii equation. The dynamic property of stable wavefunctions is numerically examined in two phase spaces when the harmonic potential is altered suddenly.The figures in the two phase spaces are regular even after a long time of interations.For negative nonlinear coefficients,two eigenvalues related to the same negative nonlinear coefficient are calculated,and the stability of the corresponding two wavefunctions is tested.

Classical trajectories of a diatomic molecule system (CO) in laser fields are calculated in the symplectic scheme. The calculated results are compared with that with Runge-Kutta (R-K) approach. The vibration trajectories, phase trajectories and vibration energy of a diatomic molecule CO are analysed.

A 9-bits lattice gas model with temperature effect is applied into the simulation of thermoacoustic prime movers. The self-excited oscillation in a thermoacoustic resonant tube has been simulated. The distribution of two-dimensional temperature field and the evolution process of temperature are presented as well. The effects of the length of stack and of its position on acoustic pressure have also been investigated numerically. The simulation results are valuable to the optimum design of stack. The validity of the lattice gas model for a thermoacoustic engine has been verified by the comparison of the simulated and experimental results, which demonstrates that the lattice gas method is suitable for the thermoacoustic simulation.

The dynamic properties of nonlinear Schrödinger equations are investigated numerically by using the symplectic scheme (Euler centered scheme). The dynamic behavior of cubic nonlinear Schrödinger equations with various nonlinear parameter is studied in different phase space.And the dynamic properties of cubic-quintic nonlinear Schrödinger equations are dealt with numerically by using the symplectic scheme. The dynamic behaviors of cubic-quintic nonlinear Schrödinger equations with different cubic and quintic nonlinear parameters are discussed in the phase space.It shows that the route varies with different cubic nonlinear parameters and with the increase of the quintic nonlinear parameters.

This paper presents the symplectic scheme-matrix algorithm for solving the vibrational and vibrational-rotational energy eigenvalues of ⁷Li₂ in A¹Σ_u⁺ state, and compares the computed results with the results calculated by Ley-Koo et al.. The results show that our method is convergent and reliable, and it is a reasonable method for computing the vibrational and vibrational-rotational energy eigenvalues of diatomic molecules. Since the symplectic scheme-matrix algorithm transforms the question of the solution of the radical equation of the diatomic molecules into that of the eigenvalues of the real tridiagonal symmetric matrix, it is more simple and needs smaller computer memory and less computing time compared with the method of expanding eigenfunctions of diatomic molecules used by Ley-Koo et al.

In a quantum system,when the Hamiltonian operator is time-dependent,"artificial" variables are introduced to construct the symplectic integrators with arbitrary high order accuracy.As an example,the time-evolution of an electron in the infinite deep potential well interacting with an animated laser field is investigated.The computed results coincide with the theory and can preserve the norm,which show that the methods are reasonable.

The multigrid method is applied in the unstructured grid. The coarse mesh is obtained by the "agglomerated" method. The Jamson's finite volume method is used for the calculation of the flow. Compared with the single mesh, the unstructured multigrid algorithm can accelerate the convergence and can improve the calculation efficiency, and the CPU time is largely reduced. The two-dimensional and three-dimensional numerical examples are presented.

For an intense field model, the time-dependent Schrødinger equation with initial and boundary conditions can be discretized into the inhomogeneous linear canonical equation by substituting the symmetric difference quotient for the partial derivative. As the general solution of its homogeneous equation and the particular solution of the inhomogeneous equation can be generalized by the symplectic transformation, it is a reasonable numerical method to use the symplectic scheme. To prove its utility, a simple example is described using the symplectic scheme and RK method, and compared with the exact solution. The results show that the solution using the symplectic scheme can preserve the intrinsic properties of the equations after a long evolution, but RK method cannot.

The symplectic algorithm in the complex symplectic space is the algorithm that preserves the Wronskian.The Wronskian calculated by using the symplectic scheme keeps unchanged which is in good agreement with theoretical analyses after a long distance of computation.The numerical solutions of the one dimensional model of strong laser field are calculated by using the Wronskian preserving and symplectic scheme.

This paper deals with a model and methods of computer random simulation of the magnetic properties of magnetic liquids. Effects of the concentration, temperature and particle size of magnetic liquids upon their magnetic properties have been investigated successfully by the calculation of reduced magnetisation of a system containing 32 magnetic particles with the model constructed.