一种可扩展的三维半导体器件并行数值模拟算法

在基于漂移-扩散模型的三维半导体器件数值模拟中,通过有限体积法进行数值离散,采用完全耦合的牛顿迭代求解非线性代数方程组,并使用基于代数多重网格预条件子的GMRES方法求解牛顿迭代中的线性方程组,构造一种稳健且高度可扩展的非结构四面体网格上求解半导体方程的并行算法.基于PHG平台实现该算法的并行计算程序,并对PN结和MOS场效应晶体管等问题进行了最大网格规模达到5亿单元、最大并行规模达到1 024进程的大规模数值模拟实验,结果表明,该算法计算效率高,可扩展性好.

A Scalable Parallel Algorithm for Three-dimensional Semiconductor Device Simulation

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.