基于第一性原理量子输运模拟的并行计算

为了解决基于第一性原理分析计算大尺度量子输运体系时遇到的耗时长久问题,挖掘密度泛函理论与非平衡格林函数相结合方法(DFT+NEGF方法)在自洽迭代过程中的计算热点,就计算电子密度矩阵时的能量点积分和计算格林函数时的矩阵求逆/乘法运算提出MPI/Open MP并行计算方案.能量点积分采用MPI多进程并行方案,在数据初始化时需要将稀疏矩阵和积分能量点依照轮询调度算法分配给各进程.矩阵求逆/乘法的并行化既可调用ScaLAPACK子程序实现又可调用IntelMKL数学库中的OpenMP多线程加速函数实现.由于不同能量点计算的独立性,能量点积分采用的MPI并行计算获得近乎线性的加速比曲线.由于Open MP多线程并行采用的是基于共享内存的数据交换机制以及线程间切换通信开销小,矩阵求逆/乘法运算的OpenMP并行实现在计算效率上要优于而在程序的可扩展性上要劣于MPI多进程并行实现.

Parallel Computing of First-principles Based Quantum Transport Simulations

To solve long time-consuming problem in analysis of large-scale quantum transport systems based on first-principles calculations, we analyze hot spots of self-consistent iterations within the framework that combines non-equilibrium Green's function with density functional theory, namely DFT+NEGF method. Two parallel computing schemes based on MPI/OpenMP are proposed to deal with energy point integration and matrix inversion/multiplication. For energy point integral parallelism, sparse matrix as well as energy points should be assigned to each process over data initialization according to round-robin scheduling algorithm. Either MPI based ScaLAPACK subroutine or OpenMP based Intel MKL subroutine can be called to realize matrix inversion/multiplication parallelization. A sub-linear speedup ratio curve is obtained for energy point integral parallelism due to the fact that calculations related with different energy points are mutually independent. OpenMP parallelism adopts shared memory patterned data exchange mechanism and overhead of switching threads is rather small, and consequently it is better in computing efficiency but worse in code scalability than MPI implementation.