共性数学库PETSc(Portable,Extensible Toolkit for Scientific Computation)是高性能计算的基础模块,是超级计算机计算环境的基础算法库之一,其性能直接影响调用数学库的高性能数值计算应用的效率.面向国际上首台100P神威·太湖之...共性数学库PETSc(Portable,Extensible Toolkit for Scientific Computation)是高性能计算的基础模块,是超级计算机计算环境的基础算法库之一,其性能直接影响调用数学库的高性能数值计算应用的效率.面向国际上首台100P神威·太湖之光异构超级计算机,根据实际研究需要选取PETSc中两个典型用例ex5(单节点线性求解方程组问题)和ex19(多节点求解2D驱动腔问题)进行实验探究.对运行结果分析找到的热点函数主要为PETSc函数库中7个核心函数,针对这7个核心函数(主要包括向量运算与矩阵运算),提出和实现了其异构并行算法,并结合机器的异构体系结构提出了相应的性能优化方法.在超级计算机上的实验结果为:核心函数并行算法在4主核、256从核的单节点上加速比最大可达到16.4;多节点情况下,当输入规模为16 384时,8192个节点相对于256节点的加速比为32,且加速比随着异构处理器数目的增加接近线性增加,表明PETSc核心函数并行算法在神威·太湖之光超级计算机上具有良好的可扩展性.展开更多
In this paper, parallel library, portable extensible toolkit for scientific computation （FETSc）, 18 used to solve linear systems in soil-water coupled finite element method （FEM） for geotechnical problems. The par...In this paper, parallel library, portable extensible toolkit for scientific computation （FETSc）, 18 used to solve linear systems in soil-water coupled finite element method （FEM） for geotechnical problems. The parallel environment is integrated into GLEAVES, which is a geotechnical software package used for the finite elementsimulation. The linear system Ax = b which is a fundamental and the most time-consuming part of the FEM is solved with iterative solvers in PETSc. In order to find a robust and effective combination of iterative solvers and corresponding preconditioners for the soil-water coupled problems, performance evaluations on Krylov subspace methods and four preconditioners are carried out. The results indicate that general minimal residual （GMRES） method coupled with preconditioners can provide an effective solution. The application to a construction project is presented to illustrate the potential of the proposed solution.展开更多
CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design.Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches...CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design.Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage.The dynamical core of the MONC atmospheric model is one example of CFD which requires the solving of the Poisson equation to determine pressure terms.Traditionally this aspect of the model has been very time consuming and so it is important to consider how we might reduce the runtime cost.In this paper we survey the different approaches implemented in MONC to perform the pressure solve.Designed to take advantage of large scale,modern,HPC machines,we are concerned with the computation and communication behaviour of the available techniques and in this text we focus on direct FFT and indirect iterative methods.In addition to describing the implementation of these techniques we illustrate on up to 32768 processor cores of a Cray XC30 both the performance and scalability of our approaches.Raw runtime is not the only measure so we also make some comments around the stability and accuracy of solution.The result of this work are a number of techniques,optimised for large scale HPC systems,and an understanding of which is most appropriate in different situations.展开更多
ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma phys...ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma physics in magnetic confinement devices;however ArbiTER should be applicable to other science and engineering fields as well.The code permits a variable numbers of dimensions,making possible application to both fluid and kinetic models.The use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.展开更多
基金the National Natural Science Foundation of China(Nos.41172251 and 41002097)
文摘In this paper, parallel library, portable extensible toolkit for scientific computation （FETSc）, 18 used to solve linear systems in soil-water coupled finite element method （FEM） for geotechnical problems. The parallel environment is integrated into GLEAVES, which is a geotechnical software package used for the finite elementsimulation. The linear system Ax = b which is a fundamental and the most time-consuming part of the FEM is solved with iterative solvers in PETSc. In order to find a robust and effective combination of iterative solvers and corresponding preconditioners for the soil-water coupled problems, performance evaluations on Krylov subspace methods and four preconditioners are carried out. The results indicate that general minimal residual （GMRES） method coupled with preconditioners can provide an effective solution. The application to a construction project is presented to illustrate the potential of the proposed solution.
文摘CFD is a ubiquitous technique central to much of computational simulation such as that required by aircraft design.Solving of the Poisson equation occurs frequently in CFD and there are a number of possible approaches one may leverage.The dynamical core of the MONC atmospheric model is one example of CFD which requires the solving of the Poisson equation to determine pressure terms.Traditionally this aspect of the model has been very time consuming and so it is important to consider how we might reduce the runtime cost.In this paper we survey the different approaches implemented in MONC to perform the pressure solve.Designed to take advantage of large scale,modern,HPC machines,we are concerned with the computation and communication behaviour of the available techniques and in this text we focus on direct FFT and indirect iterative methods.In addition to describing the implementation of these techniques we illustrate on up to 32768 processor cores of a Cray XC30 both the performance and scalability of our approaches.Raw runtime is not the only measure so we also make some comments around the stability and accuracy of solution.The result of this work are a number of techniques,optimised for large scale HPC systems,and an understanding of which is most appropriate in different situations.
文摘ArbiTER(Arbitrary Topology Equation Reader)is a new code for solving linear eigenvalue problems arising from a broad range of physics and geometry models.The primary application area envisioned is boundary plasma physics in magnetic confinement devices;however ArbiTER should be applicable to other science and engineering fields as well.The code permits a variable numbers of dimensions,making possible application to both fluid and kinetic models.The use of specialized equation and topology parsers permits a high degree of flexibility in specifying the physics and geometry.
