OPAAL: Simulation and Optimization of Casting and Extrusion Processes

工艺设计工程师必须同时控制产品的宏观和微观性能，以满足当今竞争激烈的市场需求。 控制铸造和挤压部件的材料性能（如沉淀物结构、晶粒尺寸和残余应力）与控制产品几何形状一样，对产品质量至关重要。 最终，产品和工艺设计必须被视为一个单一的耦合问题，因为决定产品形状的工艺也决定了其材料特性。 该研究计划在数学家，工程师和计算机科学家之间建立了新的合作，以实现对过程和产品设计基础的复杂非线性行为的多尺度模拟。具体来说，研究人员和他们的同事模型微观组织的发展与铸造过程中的枝晶生长和再结晶和晶界沉淀物在挤压和淬火过程中的演变。 这些多尺度仿真问题的设计优化的背景下，导致非常大的计算需求，并行解决方案的策略是必不可少的。 复杂的，随时间变化的几何形状的表示-特别是那些不断变化的拓扑结构-是另一个重大的挑战。 研究人员使用各种新的方法，从分析，计算几何和计算机科学来解决这些问题。 他们开发先进的误差估计来驱动“智能”网格生成器和自适应程序，强调由严格的数学分析支持的新几何算法，以确保准确性和可靠性。 他们设计新的编程环境以及编译时和运行时代码优化器，以生成可移植的高性能并行代码。 无网格水平集方法，时空有限元模型，和新的方法从计算几何解决几何的挑战。 研究人员探索大规模问题的新解决方法，开发并行非线性规划策略和先进的设计灵敏度分析方法，以优化加工条件和刀具几何形状。该项目推进新的计算技术，通过宏观过程控制预测和优化微观结构材料性能。 这项工作有可能对制造业产生巨大的经济影响。 用于民用和国防应用的新型高性能材料、更低成本和更环保的制造工艺、更好的质量控制以及通过虚拟工艺和产品原型缩短上市时间的能力都成为可能。 新的仿真和设计工具可帮助工程师和工艺设计人员超越当前昂贵且通常无效的试错设计方法。 特别是，实用的，易于使用的工具，用于优化工艺设计的前景，促进了这些技术在工业中的使用增加。 这一努力所产生的新的加工能力可能会导致全新的产品类别，除了现有产品线的重大改进。 与美国主要制造公司的工业科学家和工程师密切合作是这项工作的重要组成部分，因此可以确保向工业界和从工业界进行有效和及时的技术转让。 作为这项工作基础的跨学科结构，涉及数学家，工程师和计算机科学家之间的新合作，本身就是研究的一个新方面，有可能对美国大学的科学研究文化产生重大影响。 它产生了一种新的博士教育模式。为学生和博士后提供跨学科的培训，为下一个世纪的科学和技术领导者提供所需的培训。2这项活动的资金将由数学科学部、MPS跨学科活动办公室和DARPA提供。

Process design engineers must simultaneously control the macroscopic and microscopic properties of products to meet the demands of today's competitive marketplace. Control over material properties (such as precipitate structure, grain size, and residual stress) in cast and extruded components is as essential to product quality as is control over the product geometry. Ultimately, product and process design must be treated as a single coupled problem, because the processes that determine a product's shape also determine its material properties. This research initiative establishes new collaborations among mathematicians, engineers, and computer scientists to enable multiscale simulations of the complex, nonlinear behavior that underlies process and product design. Specifically, the investigators and their colleagues model microstructural development associated with dendritic growth in casting processes and with recrystallization and the evolution of grain-boundary precipitates in extrusion and quench processes. These multiscale simulation problems within the context of design optimization lead to very large computational requirements for which parallel solution strategies are essential. The representation of complex, time-varying geometries --- especially those with evolving topology --- is another significant challenge. The investigators use a variety of new methods from analysis, computational geometry and computer science to address these issues. They develop advanced error estimates to drive "smart" mesh generators and adaptive procedures, emphasizing new geometric algorithms backed by rigorous mathematical analysis to ensure accuracy and reliability. They design new programming environments as well as compile-time and run-time code optimizers to produce portable, high performance parallel codes. Gridless level set methods, space-time finite element models, and new methods from computational geometry address the geometric challenges. The investigators explore new solution techniques for large-scale problems and develop parallel nonlinear programming strategies and advanced design sensitivity analysis methods to optimize processing conditions and tool geometries.This project advances new computational technology to predict and optimize microstructural material properties via macroscopic process controls. This work has the potential for tremendous economic impact in the manufacturing sector. New high-performance materials for civilian and defense applications, lower cost and more environmentally friendly manufacturing processes, improved quality control, and the ability to reduce the time to market via virtual process and product prototyping all become possible. The new simulation and design tools help engineers and process designers to move beyond current trial-and-error design approaches that are expensive and often ineffective. In particular, the prospect of practical, easy-to-use tools for optimal process design promotes the increased use of these techniques in industry. The new processing capabilities generated by this effort could lead to entirely new product classes, in addition to substantial improvements in existing product lines. Close collaboration with industrial scientists and engineers at major U.S. manufacturing companies is an essential component of this work, so effective and timely technology transfer to and from industry is assured. The interdisciplinary structure that underlies this effort, involving new collaborations between mathematicians, engineers and computer scientists, is itself a novel aspect of the research that has potential for significant impact on the culture of scientific research at U.S. universities. It generates a new educational model for Ph.D. students and postdocs that provides the multi-disciplinary training required for scientific and technical leadership in the coming century.Funding for this activity will be provided by the Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and by DARPA.