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.

A brief introduction to development history of computational electromagnetics(CEM) and numerical methods in CEM is provided. In addition, we discuss up-to-date progress of CEM in scientific researches, commercial softwares and proprietary softwares. Considering applications of electromagnetics environmental effects (E3), we present development of our numerical simulation platform of E3. Finally, future trends of development in E3 are shown.

To overcome prohibitive cost in computational time and memory requirement in simulating groundwater flow models with detailed spatial discretization and long time period,we present an efficient massive parallel-computing program JOGFLOW for large scale groundwater flow simulation.In the program,groundwater flow process in MODFLOW is re-implemented on JASMIN by designing patch-based algorithms as well as using communication method based on adding ghost cells to each patch.Accuracy and efficiency of JOGFLOW are demonstrated in modeling a field flow located at Yanming Lake in Zhengzhou of Henan province.Parallel scalability is measured by simulating a hypothetic groundwater flow problem with much detailed spatial discretization.Compared to 32 cores,the parallel efficiency reaches 77.2% and 67.5% on 512 and 1 024 processors,respectively.Numerical modeling demonstrates good performance and scalability of JOGFLOW,which enables to support groundwater flow simulation with tens of millions of computational cells through massive parallel computing on hundreds or thousands of CPU cores.

A BNCT treating planning system MCDB is developed.Three-dimensional material matrix and tally matrix are designed, which are used to describe voxel models and tally.A fast track technique is used in simulation.Computation time is greatly decreased compared with MCNP code.Same dosimetry results with MCNP are achieved by MCDB,which is faster by 3.1-3.4 times with respect to MCNP.Computation time and accuracy of most voxels reach clinical BNCT requirement in a scale of 10 million particles.

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.

Jacobian.free Newton-Krylov(JFNK) method is analyzed and improved by using physical constraints in iteration. Consequently.physical constraints are always satisfied in iteration process of the improved JFNK method.Non。physical phenomenon is avoided.In particular.there is no negative temperature as the method is used for 2-D 3-T energy equations.Robustness of JFNK method is improved.

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.

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.

We propose a two-dimensional(2D) monotonicity-and conservation-preserving interpolation operator based on a one-dimensional monotonicity-and conservation-preserving interpolation operator.With several numerical examples we conclude that our interpolation operator is effective.Furthermore,we take it as a refinement interpolation operator in a structured adaptive mesh refinement(SAMR) algorithm to solve numerical examples governed by 2D Euler equation.Results show that our method is effective in SAMR.

We propose a data reduction approach based on information theory. It comprises sampling of datssets based on mutual entropy and truncation based on offline Marginal Utility. The approach is a universal method for multi-dimensional scientific dataset streams. To show applicability, results obtained with plasma simulation data are presented, It reduces relationship and redundancy between datesets.

We propose a monotonicity- and conservation-preserving interpolation operator, named PQIM. Its order of convergence, conservation-preserving and monotonicity-preserving properties are demonstrated. The interpolation operator is proved to restrain oscillation caused by interpolation effectively.

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.

A parallel code, with fully three-dimensional nonlinear hydrodynamics coupled with light wave propagation, is implemented to study mechanism of laser beam self-focusing and filamentation instability as high intensity laser propagates in a large size underdense plasma. Numerical method and parallel algorithms are introduced.

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.

In order to realize the parallelization of LARED-R-1,a serial code for numerical simulation of two-dimensional radiation transport,a directed graph is used to accurately describe the data dependencies.A parallel pipeline flux sweeping algorithm is applied to parallelize the code efficiently.Moreover,a special technique of buffering short messages for less communications is presented to improve the parallel performance.For a typical model discretized by 3 800 cells,100 energy groups and 40 directions,tests on a parallel machine show that the parallel LARED-R-1 achieves parallel efficiency by 80% with 64 processors and by 53% with 128 processors,respectively.

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.

It provides an overview of the parallel computing for 2-dimensional plasma simulations with particle clouds in cells methods under both shared-memory and distrbuted-memory parallel computing environments.The parallel algorithm and its implementation are desigened on the basis of the serial algorithm and the executing characteristics of the serial code.The practical parallel computations are performed under Challenge,DAWN 1000+, Power PC Cluster and XMZY. Many important conclusions are given and quite useful for the parallel computations of both types of particle simulation methods and other applicational codes.

Four different types of serial multigrid preconditioned conjugate gradient algorithms are applied to treat interface problems, and their numerical convergence rates are also compared with respect to interface types, interface degree and stepsize. Schwarz parallelism is used for algorithms, and discussion concerns the convergence rates with respect to the number of subdomains, and the benefits owing to Schwarz parallelism. Detailed performence results are also given.