COLLABORATIVE RESEARCH:DEVELOPMENT OF EFFICIENT PETASCALE ALGORITHMS FOR INHOMOGENEOUSQUANTUM-MECHANICAL SYSTEMS

该奖项是根据2009年《美国复苏和再投资法案》(公法111-5)提供资金的。随着新的超级计算机的出现，这些计算机使用了数十万个处理器，计算速度接近每秒1千万亿次，许多重大的科学问题可以被解决，这些问题在几年前还无法解决。这个由物理学家和计算机科学家组成的团队将基于所谓的Lanczos方法开发新的计算算法，该方法涉及使用稀疏矩阵的幂乘以初始向量，该方法将找到大型稀疏矩阵的逆矩阵的对角线，并将找到所有特征值和特征向量。开发的代码将考虑到与试图在如此大型的机器上高效运行这些代码相关的特定存储器寻址和访问问题。这些数值算法很可能在科学界得到广泛使用，将应用于这项工作中的两个难解决的科学问题。第一个是描述放置在所谓的光学晶格上的超冷原子是如何以量子力学的方式相互作用的。这个团队将与这一领域的一群世界领先的实验小组合作，解决与这些系统的行为相关的一些理论和计算问题。这些问题本质上是困难的，因为原子被放置在陷阱中，就像坐在碗里的粒子一样，这使得现有的技术很难在这些系统上使用。第二个问题是量子自旋玻璃的行为。呆板的行为是一个内在的难题，因为这种无序打破了系统的周期性，并使其具有挑战性。像量子蒙特卡罗模拟这样的传统方法由于自旋的受挫性质而失败。我们的工作基于能够描述低温性质的高温级数展开的扩展，将使人们能够准确地探索这些迷人的系统的基态性质，这些系统被认为表现出拓扑顺序或紧急合作行为。团队还将调查与使用现代并行编程模型相关的生产率权衡，例如分区全局地址空间(PGAS)，特别是UPC，来解决这类问题。根据该授权开发的通用数字代码将通过GNU公共许可证分发。该项目还将培训更年轻的研究人员进行大规模科学计算。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). With the advent of new supercomputers that employ hundreds of thousands of processors and can compute at speeds approaching one quadrillion operations per second, many grand challenge science problems can be solved which were unsolvable even a few years ago. This team of physicists and computer scientists will develop new computational algorithms based on the so-called Lanczos method, which involves using powers of a sparse matrix multiplying an initial vector, that will find the diagonal of the inverse of large sparse matrices and will find all of the eigenvalues and eigenvectors. The codes that are developed will take into account the specific memory addressing and accessing issues associated with trying to run these codes efficiently on such large machines.These numerical algorithms, which are likely to have wide use within the scientific community, will be applied to two hard scientific problems in this work. The first is to describe how ultracold atoms placed on a so-called optical lattice, where the atoms move along a corrugated "egg-carton-like" surface, interact with each other quantum-mechanically. Working with a group of the world's leading experimental groups in this area, this team will solve a number of theoretical and computational problems related to the behavior of these systems. The problems are inherently difficult because the atoms are placed in a trap, like particles sitting in a bowl, which makes established techniques very difficult to employ on these systems. The second problem is the behavior of a quantum spin glass. Glassy behavior is an inherently difficult problem, because the disorder breaks the periodicity of the system, and makes it challenging to solve. Conventional methods like quantum Monte Carlo simulations fail due to the frustrated nature of the spins. Our work, based on an extension of high temperature series expansions to be able to describe low-temperature properties, will allow one to accurately probe the ground state properties of these fascinating systems which are believed to display either topological order or emergent cooperative behavior.The team will also investigate the productivity trade offs associated with the use of modern parallel programming models, such as the partitioned global address space (PGAS), particularly UPC, for this class of problems. The general purpose numerical codes developed under this grant will be distributed via the GNU public license. This project will also train younger researchers in large scale scientific computing.