CDS&E: DFT-informed Topology Optimization Upscaling: An Accelerated Fixed-point Iteration Approach

工程设计推动经济繁荣和生活质量。 世界是由复杂的动力系统组成的，从天气和自然灾害到金融系统和人类健康。 工程设计使产品，系统和网络的开发，使我们能够蓬勃发展，并满足新兴的挑战和机遇。 由于设计涉及许多变量之间的权衡，有效的设计必须解决多个尺度上的冲突，并了解妥协如何影响动态系统的性能。像拓扑优化这样的工具可以指导关键设计概念的开发，但可能具有较高的计算成本。该项目推进基础研究，以创建高效的求解器，从而以显著降低的成本进行大规模模拟，从而能够发现在能源，医疗保健和航空航天等领域具有新特性的先进系统，并在科学和工程领域具有广泛的适用性。 该项目将培训研究生、本科生和高中生，并设计新的研究生课程。 从研究中获得的知识将通过社会媒体和组织会议专题讨论会广泛传播。该项目将为线性和非线性方程组创建新的高效和可扩展的求解器，从而能够解决前所未有的系统规模。 具体来说，方程组将重新制定为固定点的问题，这将加快使用本项目中设计的新颖，高效，准确的外推算法。 这些方法的并行实现将被开发，可以有效地使用大规模分布式存储器的计算机体系结构。研究人员还将为密度泛函理论（DFT）和拓扑优化制定线性缩放方法和可扩展的并行实现，这些方法将被集成以形成一种新的多尺度方法，用于设计具有定制特性的新结构。在这个过程中，材料行为的定律将从量子力学的第一原理中获得，没有特别的近似。总的来说，线性标度DFT方法将能够在无与伦比的长度和时间尺度上精确研究凝聚态系统。执行大规模从头算拓扑优化的能力将增强实现高分辨率、精确设计的能力，这些设计可以在实际工程应用中实现。

Engineering design drives economic prosperity and the quality of life. The world is comprised of complex dynamical systems from weather and natural disasters to financial systems and human health. Engineering design enables the development of products, systems and networks that allow us to thrive and to meet emerging challenges and opportunities. Since design involves trade-offs among many variables, an effective design must resolve conflicts at multiple scales and understand how the compromises affect the dynamical systems performance. A tool like topology optimization can guide the development of key design concepts but may have high computational costs. This project advances fundamental research to create efficient solvers that allow large-scale simulations at significantly reduced cost, thereby enabling the discovery of advanced systems with novel properties in areas such as energy, health care, and aerospace and with broad applicability across science and engineering. The project will train graduate, undergraduate, and high school students and design new graduate curriculum. The knowledge gained from the research will be broadly disseminated through social media and by organizing conference symposia. This project will create new efficient and scalable solvers for linear and nonlinear systems of equations that enable the solution of systems of unprecedented size. Specifically, the systems of equations will be reformulated as fixed-point problems, which will be accelerated using the novel, efficient, and accurate extrapolation algorithms designed in this project. Parallel implementations of these approaches will be developed that can efficiently use large-scale distributed memory computer architectures. The researchers will also formulate linear-scaling approaches and scalable parallel implementations for Density Functional Theory (DFT) and topology optimization, which will be integrated to form a novel multiscale method for the design of new structures with tailored properties. In this process, laws for material behavior will be obtained from the first principles of quantum mechanics, with no ad-hoc approximations. Overall, the linear scaling DFT method will enable the accurate study of condensed matter systems at unparalleled length and time scales. The ability to perform large-scale ab-initio informed topology optimization will enhance the capacity to achieve high-resolution, accurate designs that can be realized in practical engineering applications.