A finite difference method is used for high-order numerical solution of two-dimensional unsteady semilinear diffusion reaction equation. The spatial derivative term is discretized by a fourth-order compact difference formula, and the time derivative term is discretized by a fourth-order backward Euler formula. An unconditionally stable high-order five-level fully implicit scheme is proposed. Truncation error of the scheme is O(τ⁴+τ²h²+h⁴), that is, the time and space have fourth-order accuracy. In calculation of start-up steps, the first, second and third time levels are discretized by Crank-Nicolson method. Richardson extrapolation formula was used to extrapolate startup time accuracy to the fourth-order. A multigrid method based on the scheme is established, which accelerates convergence speed of the algebraic equations on each time level and improves computational efficiency. Finally, accuracy, stability and efficiency of the scheme and multigrid approach are verified with numerical experiments.

Electronic structure and magnetic structures of BaTi₂Bi₂O are studied with first-principles calculations.In nonmagnetic state,density of states at Fermi level are mostly derived from d_z²,d_x²-y² and d_xy orbitals.Fermi surface (FS) consists of three sheets.The third FS sheet (along X-R line) nests with the first FS sheet (along M-A line) by q-vector q₁=(π/a,0,0) or q₂=(0,π/a,0) shift.Calculated bare susceptibility χ₀(q) peaked at X-point,rather than at M-point in Fe As-based superconductors.Such peaked susceptibility induces spin density wave (SDW).Magnetic ground state is nearly two degenerate antiferromagnetism of bi-collinear antiferromagnetism (AF3) and blocked checkerboard antiferromagnetism (AF4).Peak of susceptibility χ₀(q) is obviously suppressed and becomes slightly in-commensurate with hole doping,but increased with electron doping.As spin fluctuation is suppressed superconductivity appears.It explains that superconductivity appears only in hole-doped compounds,and not in electron-doped ones.

We illustrate a technique of ray tracing by shooting method and analyze rules of ray in VTI coal. With mixed-language programming of VC ++ and Fortran, ray tracing in VTI coal with a complex velocity model is realized. It demonstrates necessaries of anisotropic ray tracing in VTI coal by comparison of ray tracing in VTI coal and isotropic media. By contrast of calculation time, it indicates that this method is efficient to meet needs of seismic records forward. The technique can be used in multi-wave ray tracing in anisotropic coal as giving responding formulae and parameters.

A scalable parallel algorithm for three-dimensional semiconductor device simulation on unstructured tetrahedral meshes using drift-diffusion model is proposed,which is characterized by finite volume discretization,fully coupled Newton iterations for discretized nonlinear equations,and GMRES iterations using algebraic multigrid(AMG) preconditioner for linear equations in Newton iterations.The algorithm was implemented using a parallel adaptive finite element toolbox PHG.Large scale parallel numerical experiments with several problems,including PN diode and MOSFET,were carried out.In numerical simulations the largest mesh size are 500 million elements and the largest number of MPI processes used are 1 024.It shows that the proposed algorithm is efficient,robust and highly scalable.

A general Godunov finite difference scheme—WENO(Weighted Essentially Non-Oscillatory) scheme with fifth-order accuracy is used to calculate 2-dimensional axis symmetrical laser-supported plasma flow field under laser ablated solid target,considering ionization degree of plasma and the interaction and coupling between laser beam and plasma.Evolution of the ablation plasma due to the interaction between laser and solid target is obtained.The simulation shows that the laser beam is strong absorbed by plasma on target surface,and the velocity of LSD(Laser Supported Detonation) wave is half of the ideal LSD derived with C-J detonation theory.

We examine the super compact symmetric finite difference scheme (SCSFD) and compare it with traditional difference methods and compact difference methods. The result shows high efficiency of SCSFD. According to the characteristics of the algorithm, a parallel algorithm named block pipelined method for three-dimensional compressible Navier-Stokes equations using SCSFD is designed and its parallel performance is analysed. Numerical experiments are carried out.

We present a parallel bisection mesh refinement algorithm based on ALBERT (Adaptive multi-Level finite element toolbox using Bisection refinement and Error control by Residual Techniques). The goal is to develop a parallel adaptive finite element code suitable for distributed memory parallel computers or PC clusters. An overview on the basic strategy for the parallelization of ALBERT is given. Issues on the parallel mesh refinement are addressed. A modified mesh refinement algorithm, which can be implemented efficiently on distributed memory parallel computers, is proposed and its properties are discussed. Numerical experiments with parallel bisection mesh refinement algorithm are shown.

Based on the high accuracy compact difference scheme and the alternating group explicit (AGE) iterative method which has obvious property of parallelism,an AGE iterative method with the fourth-order compact scheme is established for the steady convection-diffusion equation.Numerical solutions are obtained for the model problem of natural convection in a square cavity with large Rayleigh number of physical interest and small Prandtl numbers attempted.Some results of the present are compared with the referenced paper.

A simple method to calculate electrostatic fields of ion optical system and trajectories of ions in the field is discussed.The optimization methods to save disk space and accelerate the calculation process are given under condition of maintaining the calculation precision.A feasible method for searching the over-relaxation factor is present.The calculation method is applied to the calculation of a design of gridless high-resolution reflectron time-of-flight mass spectrometer.The results of the distribution of electrostatic fields,the ion trajectories and the best conditions of the fields are present.The system is adjusted to its fairly good working condition based upon these results,and mass spectra with much higher resolution are observed.

This paper presents some preliminary work on the application of Schwarz alternating method, combined with a multigrid solver, for solving the steady 2D viscous incompressible Navier-Stokes equations. The difficulty caused by the violation of the compatibility condition imposed on the normal velocity at the boundary, which arises when subdomain problems are not solved exactly at each iteration, is surrounded by adding artificial compressiblity constants to the continuity equation each time when a subdomain problem is to be solved. These constants permit to maintain the compatibility condition of the subdomain problems and one can easily show that they tend to zero when the iteration number tends to infinity (in fact, they can be expressed explicitly as functions of the iteration number and some geometrical parameters of the computational domain). Numerical experiences have been made for flows in a channel with a facing step.