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.

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.

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.

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.