(AREA: Numerical Computing and Optimization): Numerical Linear Algebra Problems and Quantum Chromodynamics

（领域：数值计算和优化）：数值线性代数问题和量子色动力学

• 批准号: 0728915
• 负责人: Andreas Stathopoulos
• 金额: $ 20万
• 依托单位: College of William and Mary
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-10-01 至 2011-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0728915&HistoricalAwards=false
• 关键词: AREA; Numerical; Computing; Optimization; Linear

Lattice Quantum Chromodynamics (QCD) is one of the world's topconsumers of supercomputer cycles. As with many other applications,the computational bottlenecks are traced to numerical linear algebraproblems. Lattice QCD gives rise to Hermitian matrix problems, wheremethods such as Conjugate Gradient (CG) or Lanczos convergeoptimally. Yet, the matrices are of enormous size, and preconditionersthat speedup convergence by more than a factor of two or three havebeen elusive. Equally important, lattice QCD involves two of the stilloutstanding problems in numerical linear algebra: to find methods thatsolve optimally a linear system with multiple right hand sides and aneigenvalue problem for a large number of eigenpairs. This research aims at developing new methods, theory, andsoftware that address the above numerical linear algebra problems,both in general and as guided by the physics of the particular QCDproblems, thereby speeding considerably lattice QCD computations andenabling further understanding of the structure of matter. The key contribution of this research is to provide a unified view oflinear system and eigenvalue methods that leads to algorithms thatsolve both problems at once in a nearly optimal way. The investigatorsstudy new numerical techniques for efficient computation of quarkpropagators in lattice QCD and extend them for improving theefficiency of Hybrid Monte Carlo. They explore a new CG method that usespreviously developed recurrence-like restarting to obtain eigenvectorsand use the method to share information between successive correctionequations in the Jacobi-Davidson eigensolvers. Finally the investigatorsdevelop well designed, tuned implementations of the above methods to theChroma package for lattice QCD, and to the state-of-the-art eigenvaluepackage PRIMME.

格子量子色动力学(QCD)是世界上最大的超级计算机周期消耗者之一。与许多其他应用程序一样，计算瓶颈可追溯到数值线性代数问题。格子QCD产生了厄米矩阵问题，而像共轭梯度(CG)或Lanczos等方法是最优收敛的。然而，矩阵的规模是巨大的，而将收敛速度加快两三倍以上的先决条件一直难以捉摸。同样重要的是，格QCD涉及数值线性代数中两个仍然悬而未决的问题：寻找最优解具有多个右端的线性系统的方法和寻找大量特征对的一个特征值问题。这项研究旨在开发新的方法、理论和软件来解决上述数值线性代数问题，既有一般的，也有特定的QCD问题的物理学指导的，从而大大加快了格子QCD的计算速度，并使人们能够进一步了解物质的结构。这项研究的主要贡献是提供了一个统一的线性系统和特征值方法的观点，从而导致以几乎最优的方式同时解决这两个问题的算法。为了有效地计算格子QCD中的夸克传播子，研究人员研究了新的数值方法，并将其推广到改进混合蒙特卡罗方法的效率。他们探索了一种新的CG方法，该方法使用先前开发的类递归重新开始来获得特征向量，并使用该方法在Jacobi-Davidson特征解算器中的连续校正方程之间共享信息。最后，研究人员开发了上述方法在晶格QCD的色度包和最先进的本征值包PRIMME上的精心设计和调整的实现。