ITR: Advances of Core Numerical Linear Algebra Techniques for Quantum Simulations in Solid State Physics

该奖项是根据ITR招标NSF-02-168提交的“小型”类别提案而颁发的。该补助金由材料研究和数学科学部门共同资助。它支持大规模矩阵计算优化的跨学科研究和教育，这是计算科学中一个长期存在的问题，在计算凝聚态和材料物理等许多领域都有重要应用。研究工作涉及计算机科学，数学和凝聚态物理学。虽然已经取得了很大的进展，利用矩阵的特殊性质或其条目的稀疏模式，仍然需要更强大和有效的方法，包括预处理技术，以改善迭代解决方案。模拟相互作用的量子系统，一个强大的方法来理解许多基本性质的材料，是这些方法的一个重要应用。它提供了动力，本研究开发强大的和有效的线性代数求解器的二次型问题和多长度尺度结构矩阵。这项研究对通过理论和模拟的应用来预测材料的性质（例如晶格结构、磁性和晶格动力学）的能力具有潜在的高度影响。该奖项还支持本科生和研究生的教育以及博士后研究人员的高级培训。%%%

This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. This grant is funded jointly by the Divisions of Materials Research and Mathematical Sciences. It supports interdisciplinary research and education on the optimization of large-scale matrix computations, a long-standing problem in computational science with important applications to computational condensed matter and materials physics and many other fields. The research effort involves computer science, mathematics, and condensed matter physics. While much progress has been made by exploiting special properties of a matrix or the sparsity pattern of its entries, the need remains for more robust and effective methods, including preconditioning techniques to improve iterative solutions. Simulating interacting quantum systems, a powerful approach for understanding many fundamental properties of materials, is an important application of these methods. It provides motivation for this research on developing robust and efficient linear algebra solvers for quadratic form problems and for multi-length scale structured matrices. This research has a potentially high impact on the ability to predict properties of materials, such as lattice structures, magnetic properties, and lattice dynamics, through the application of theory and simulation. This award also supports education of undergraduate and graduate students and advanced training of a postdoctoral researcher. %%%