OPAAL: Integrated Design, Modeling, and Simulation

集成的设计、建模和仿真在最高级别上，工程设计的过程是：给定所需的功能，综合、改进和描述具有所需功能的设备。要构建支持设计者和工程师完成这项任务的计算环境-随着工程复杂性的持续增长-需要新的集成建模、模拟、可视化和设计环境。要做到真正的预测性，它们必须有充分的数学基础，能够优雅地扩展到大型问题规模，并可靠地模拟各种范围内的物理行为。研究团队代表计算机科学、数学、机械工程、控制和动力系统以及工程设计，以开发能够协调解决这些问题的全新表示和算法。他们采用的核心集成原理是“多分辨率”的数学，即几何、数值求解器、力学和概念设计在不同分辨率水平上的描述。这种技术方法是基于细分几何的使用，并结合薄壳方程动力学。集成自动模型简化技术--包括几何、拓扑和力学--基于严格的数学和动力学原理，使它们能够在从微观行为到总体行为的广泛物理范围内准确而高效地对复杂组件的行为进行建模。在许多物理尺度上流畅而准确地移动使得这些表示和算法非常适合于工程设计。将它们与基于集合的设计方法相结合，使设计师和工程师能够快速探索大型设计空间。拟议研究的目标是根据需要显著改进建模、仿真和设计环境，例如飞机和汽车行业(以及许多其他行业)。目前的行业实践是基于单独开发的、通常不兼容的计算模块，用于几何建模、物理模拟和分析。随着现代工程的日益复杂，这种方法产生的开销越来越大，最终产生的结果物理精度令人怀疑。从头开始重新考虑这类系统的数学、物理和计算机科学基础，雇用一个由研究人员和学生组成的综合团队，可以从根本上推动工程设计的最先进水平。团队成员之间的相互作用已经产生了一种模拟金属薄板行为的新方法，消除了力学模拟中的一个长期存在的问题，并有可能彻底改变计算机模拟在这一领域的使用。为了确保他们的工作与实际工业实践的相关性，研究人员正在与飞机行业和计算机建模应用程序供应商密切合作。博士后学者、研究生和本科生被整合到这个跨学科的项目中。新一代的研究人员和从业者正在接受教育，他们同样擅长数学、计算机科学和机械工程问题。这项活动的资金将由数学科学部、MPS多学科活动办公室和DARPA提供。

Integrated Design, Modeling, and SimulationAt the highest level, the process of engineering design is: given a desired functionality, synthesize, refine, and describe a device which robustly exhibits the desired function. To build computational environments which support the designer and engineer in this task --- as the complexity of engineering continues to grow --- requires new, integrated modeling, simulation, visualization, and design environments. To be truly predictive they must be mathematically well-founded, scale gracefully to large problem sizes, and reliably model physical behavior across a wide range of scales. The research team represents computer science, mathematics, mechanical engineering, control and dynamical systems, and engineering design, to develop wholly new representations and algorithms, capable of addressing these issues in concert. The core integrating principle they employ is the mathematics of "multiresolution," i.e., descriptions at different levels of resolution, for geometry, numerical solvers, mechanics, and conceptual design. The technical approach is based on the use of subdivision geometry, coupled with thin shell equation dynamics. Integrating automatic model reduction techniques --- encompassing geometry, topology, and mechanics --- based on rigorous mathematics and dynamics principles allows them to accurately and efficiently model the behavior of complex assemblies across a wide range of physical scales from microscopic to gross behavior. Fluidly and accurately moving across many physical scales makes these representations and algorithms highly suitable for engineering design. Coupling them with set-based design methods allows designers and engineers to rapidly explore large design spaces.The objective of the proposed research is to significantly advance modeling, simulation, and design environments as needed in, for example, the aircraft and automobile industries (among many others). Current industry practice is based on separately developed, often incompatible computational modules for geometric modeling, physical simulation, and analysis. With the increasing complexity of modern engineering, this approach incurs ever larger overhead and ultimately yields results whose physical accuracy is questionable. Reconsidering the mathematical, physical, and computer science foundations of such systems from scratch, employing an integrated team of researchers and students, can radically advance the state of the art in engineering design. Cross fertilization among the team members is already yielding a new approach to simulating the behavior of thin sheets of metal, removing a long standing problem in mechanics simulation, with the potential to revolutionize the use of computer simulations in this area. To ensure the relevance of their work to real industrial practice the researchers are collaborating closely with aircraft industry and vendors of computer modeling applications. Postdoctoral scholars, graduate students and undergraduates are integrated into this crossdisciplinary program. A new generation of researchers and practitioners is being educated who are equally at ease with questions of mathematics, computer science, and mechanical engineering.Funding for this activity will be provided by the Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and by DARPA.