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”类提案获得的。该基金由材料研究部和数学科学部联合资助。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，在计算凝聚态物质和材料物理以及许多其他领域具有重要应用。研究工作涉及计算机科学、数学和凝聚态物理。虽然通过利用矩阵的特殊性质或其条目的稀疏模式已经取得了很大进展，但仍然需要更健壮和有效的方法，包括预处理技术来改进迭代解。模拟相互作用的量子系统是理解材料许多基本性质的有力途径，是这些方法的重要应用。这为研究开发二次型问题和多长度尺度结构矩阵的鲁棒高效线性代数求解器提供了动力。这项研究通过理论和模拟的应用，对预测材料性质（如晶格结构、磁性和晶格动力学）的能力具有潜在的高影响。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. %%%