ITR: New Algorithms for Scalable Modeling in Materials Science

上个世纪最重要的成就之一是发展了预测物质电子和结构性质的精确方法。这些方法，基于密度泛函理论和赝势，使我们能够探索材料的性质，而不诉诸实验。我们现在可以根据数值计算预测新材料及其特性。这些方法的唯一固有限制是计算限制;当前的电子结构方法具有非常高的计算成本。虽然现代高性能计算机的使用使这些问题的原始计算能力取得了巨大进步，但算法方面的增益也是必要的，以适应更复杂的材料。本项目将介绍基于高效算法的新方法，以绕过上述计算限制。它将寻求新的解决方案方法，提高效率，而不牺牲准确性和功能。特别地，一个目标将是避免使用特征向量，这是计算和存储器的主要成本。该项目将通过检查问题的基本物理来做到这一点，这表明可以计算并使用由相同特征向量所跨越的子空间的不同基础。该项目将找到有效和强大的方法来计算这些基础，找到有效的解决方案，时间依赖性和自洽的Kohn-Sham方程，开发有效的核外并行方法来解决这些非常大的系统，并使用这些方法来执行真实的材料的开创性计算。

)One of the most significant achievements of the last century has been the development of accurate methods to predict the electronic and structural properties of matter. These methods, based on density functional theory and pseudopotentials, allow us to explore the properties of materials without resort to experiments. We can now predict new materials and their properties based on numerical calculations. The only inherent limitations of these methods are computational constraints; current electronic structures methods have a very high computational cost. While the use of modern high-performance computers has enabled tremendous progress in raw computational power for these problems, gains on the algorithms side are also necessary to accommodate more complex materials.This project will introduce new methods, based on efficient algorithms, for bypassing the computational limitations mentioned above. It will seek novel solution methodologies that improve efficiency without sacrificing accuracy and functionality. In particular, one goal will be to avoid the use of eigenvectors, the primary cost for both computation and memory. The project will do this by examining the fundamental physics of the problem, which reveals that a different basis for the subspace spanned by the same eigenvectors can be computed and used instead. The project will find efficient and robust methods for computing these bases, find efficient solutions to the time-dependent and self-consistent Kohn-Sham equations, develop effective out-of-core parallel methods for solving these very large systems, and use these methods to perform pioneering calculations of real materials.