System in package (SiP) is mainstream technology in the design of electronics system. Numerical simulation plays an important role in SiP applications. However, due to the specific complexity of SiP applications, existing algorithms for linear systems arising from time-harmonic Maxwell's equations are faced with great challenges, which become a bottleneck restricting efficiency of large-scale numerical simulations. In this paper, we review algorithms for time-harmonic Maxwell's equations in SiP applications. Based on capability assessment of existing algorithms for realistic SiP models, we propose a preconditioning strategy, and show its feasibility and efficiency. Furthermore, we analyze impact of such applications on performance behavior of current algorithms and the challenges we faced with.

Interaction between magnetic field and fluids is crucial in Z pinch process. Since Z pinch involves with multi materials and severe deformation, we develop 3D compatible Lagrangian staggered and cell-centered schemes for ideal MHD on unstructured meshes. Both of the schemes are of first order in space and time discretization. Accuracy and robustness of the schemes are validated with typical numerical tests.

With multiple scattering theory of electrons we studied energy deposition of electrons within target and energy distribution on spot of X-ray production by Monte Carlo method as energetic electrons impinge into target vertically. It shows that spread of electrons within target is relevant to incident electron energy and target material. And 99% electron energy is deposited in a cylindrical zone. Energy deposition of electrons along incident direction increased with depth first, and then to a certain depth it decreased rapidly, which is in accordance with electron backscattering theory. These results illustrate that X-ray production zone is within a certain depth under target surface. In addition, simulation results of diamond indicate that diamond film is not recommended as an electron absorption grating, but as an excellent heat sink of target. It can be used as reference for design of microstructure X-ray tubes.

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.

We analyze approximation and propose a two-level algorithm for finite volume schemes of diffusion equations with structured adaptive mesh refinement. First of all, a typically conservative finite volume scheme was discussed, along with criterion for refining and coarsening interpolation operator. Secondly, non-conforming elements around coarse-fine interface were eliminated by introducing auxiliary triangle elements. A symmetric finite volume element (SFVE) scheme was designed. And further analysis showed the scheme has better approximation. It weakens restrictions. Finally, a two-level algorithm was constructed for SFVE. Theoretical analysis and numerical experiments demonstrate uniform convergence of the algorithm.

We consider solution of diffusion equations using structured adaptive mesh refinement(SAMR).In SAMR hierarchy, each level is organized as a union of uniform rectangular patches.An implicit time-integration algorithm with temporal refinement strategy is shown.In the algorithm,timestepping advances from the coarsest level to the finest level sequentially,and a multilevel synchronization process is required for fixing fluxes dismatch at coarse-fine interface.A criterion for algorithm complexity is introduced. Numerical results show validation and performance of the algorithm.Finally,the algorithm is applied to radiation hydrodynamics simulations,where nonlinear non-equilibrium radiation diffusion equations are solved.Simulation result shows that,compared with uniform refinement mesh,performance of the method is improved by 33 times.

Performance of physical-variable based coarsening two-level(PCTL) preconditioner is analyzed for typical linear systems discretizated from two-dimensional(2-D) radiative diffusion equations with photon,electron,ion temperatures(3-T).It reveals that performance of PCTL strongly depends on both coupling of three temperatures and diagonally dominance of three diagonal sub-matrices of coefficient matrix.An adaptive algorithm for sub linear systems in PCTL is proposed.Numerical results show efficiency and robustness of the method.For 37 2-D 3-T linear systems in simulations,PCTL based on the algorithm speeds up 2.5 times compared with classical algebraic multigrid (AMG) preconditioners.

Cooling field dependence of exchange anisetropy Was investigated in ferromagnetic(FM)/antiferromagnetic(AFM) bilayers with antiferromngnetle interface coupling. It shows that the exchange bias H_E Can change from negative to positive with increasing cooling field H_CF and cooreivity H_C acquires a maximum near crossover of H_E.Especially.effect of FM and AFM thickness on exchange anisotropy is discussed in detail.Both negative(or positive)H_E and H_C always decrease with increasing of FM thickness t_FM,which shows good agreement with experimental observation.It demonstrates interfacial nature of the exchange anisotropy.However,AFM thickness t_AFM dependence of exchange anisotropy is relatively complex.In the case of positive H_E,with increasing of t_FM,H_E increases and H_c decreases.But。in the valse of negative H_E,H_E decreases and H_C increases with increasing t_AFM.

An adaptive time integration algorithm is proposed for ADE(alternating direction explicit based on dimension splitting) scheme.Based on the algorithm,a parallel adaptive program for multi-material hydrodynamics is developed on JASMIN.An implosion experiment in ICF(inertial confinement fusion) is simulated on 512 processors.Both simulation results and performance analysis demonstrate correctness and efficiency of the algorithm and the code.

Tension simulations of[001]monocrystalline face-centered cubic SiC(β-SiC) and C-doped β-SiC bulks are performed with molecular dynamics method to investigate intrinsic deformation mechanisms and mechanical behaviors of β-SiC under strain rates of 5×10⁸/s,1×10⁹/s,1×10¹⁰/s.It is found that Si-C sp³ and C-C sp³ bonds respectively transform to Si-C sp² and C-C sp² bonds as soon as the strains reach certain critical values.As certain amounts of sp² bonds are formed,instable fractures emerge in β-SiC.Since C-C sp² bonds are formed earlier than Si-C sp² bonds,the doping of C elements leads to the decrease of strength,Young's modulus and tension fracture strain of β-SiC.In addition,it is found that the strain rates have effects on tensile-strength,but not on Young's modulus.

In a diffusion-limited aggregation model with spin freedom in each particle,morphology and fractal dimension D_f of magnetic clusters grown on two-dimensional triangular lattices are investigated with Monte Carlo study.Power-law interaction J/r^a is used.It shows that as α≥5 patterns of clusters hardly vary with J.Their fractal dimensions range from 1.50 to 1.70.With decreasing α,morphology evolution of clusters exhibits rich behaviors.Fractal dimension D_f changes continuously from about 1.20 to 1.90.

Phases of antiferromagnetic magnetization and exchange bias and coercivity in ferromagnetic/antiferromagnetic/ferromagnetic(FM/AF/FM) trilayers with interface quadratic and biquadratic exchange coupling are studied comprehensively.Three possible cases are found,namely reversible recovering case,irreversible continuously-reversing case and irreversible discontinuously-reversing case. Realization of the cases strongly depends on pinned-M_FM interface quadratic exchange coupling J₁,free-M_FM interface quadratic exchange coupling J₂ and biquadratic coupling J'₂.In the reversible recovering,the exchange coupling results in an exchange bias,and there is no exchange bias in other cases.It provides possible explanation for both hysteresis energy loss and perpendicular coupling at the interface.

Binding energy of substrate,coupling energy of nearest neighbor particles and strain field are introduced to diffusion barrier.Cluster growth process at different temperatures is investigated with Monte Carlo simulation.It shows that as 400 K≤T ≤ 480 K the average width of ramified clusters is independent on temperature T and is almost equal to the diameter of single particle.As 500 K≤T ≤ 680 K,however,width of the ramified cluster increases gradually to that of 4 particles with increasing temperature.As T increases further,clusters with large number of particles disappear,due to strong activity of particles.Average number of particles in each cluster is smaller than 2.Evolution of cluster morphology during growth process and number of cluster at temperatures are studied as well.

A two-level iterative method is proposed for linear systems discretizated from two-dimensional(2-D) radiative diffusion equations with photon, electron,ion temperatures(3-T).The main idea is to decouple one temperature from other two by a special coarsening strategy.Variables related to electron temperature are forced to be selected as coarse points and photon and ion temperatures are forced to be fine points.Several single temperature equations instead of coupled linear systems need to be solved by a classical-AMG method.The method is applied to the JFNK framework for preconditioning.Numerical results show effectiveness of the method.

We analyze scalability of parallel algebraic multigrid algorithms for large sparse linear systems.To analyze performance of the parallel iterative algorithm and its implementation,a method for analyzing scalability of parallel computing is presented. Numerical results show that the average stencil size of the grid operator and the convergence efficiency are keys in the parallel algebraic multigrid method.

As 2-D 3-T heat conduct equations are discretized in a fully implicit method,it is very difficult to solve the nonlinear algebraic equations obtained due to strong nonlinearity.Efficient initial guesses for iterative solutions of discretized nonlinear algebraic equations are presented.Numerical results for two media with different properties show that the proposed initial guesses improve computational efficiency and reduce the influence of nonlinear solver on the time step as well.

Two finite difference three-level alternating methods for the two-dimensional heat equation on a structured triangular mesh are obtained numerically. They are ABd( Alternating Band) and ABdE-I(Ahernating Band Explicit-Implicit) methods. An alternating technique using different schemes in neighboring time levels and spatial domain is employed. A theoretical analysis and numerical experiments demonstrate that both methods show obvious parallelism, good accuracy and unconditional stability.

The laminar flamelet model in combination with joint probability density function (PDF) transport equation of mixture fraction and turbulence frequency is used to simulate fluctuating behavior of radiative source term in turbulent jet diffusion flames of hydrogen.The frequency distributions of radiative source terms in the combustion zone are calculated. The results show that, for the given ensemble, about 95% samples of radiative source term locate within the region of ±3.0 standard deviation of the mean radiative source term. The profile of frequency distribution indicates having a single peak.

The high specific activity isotopes:¹⁹²Ir and ⁶⁰Co in the high neutron flux reactor are calculated with the method of reactor physics.The results of calculation are analyzed in two aspects:the production of isotopes and the influence to parameters of the reactor,and hence a better case is proposed as a reference to the production.