CRII: CHS: A Plug-and-Play Deformable Model Based on Extended Domain Decomposition

CRII：CHS：基于扩展域分解的即插即用变形模型

• 批准号: 1464306
• 负责人: Yin Yang
• 金额: $ 17.48万
• 依托单位: University of New Mexico
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-03-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1464306&HistoricalAwards=false
• 关键词: CRII; CHS; Plug; Play; Deformable

Advances in data acquisition tools have led to a dramatic increase in the geometric complexity of 3D data. Efficiently modeling, simulating, and analyzing these scanned large-scale real-world models become a serious challenge, because the numerical integration of high dimensional partial differential equations (over millions of degrees of freedom) is prohibitive for time-critical applications such as surgical simulation, bio-medical imaging, virtual/augmented reality, and physically-based animation. The problem becomes significantly more acute in situations where the rest-shape geometries of the 3D models are frequently altered and there is a need for collision detection/response coupled with high fidelity visualization of heterogeneous material properties and efficient transmission over the network to facilitate collaborative interaction. In this project the PI will address this challenge by developing a research program to create a modularized computational framework for efficient deformable simulation by partitioning the deformable body into small-size domains and re-connecting them back using weakened linkages. Domain-level computations are independent and reusable; thus, the expensive deformable simulation is reframed as a plug-and-play computational assemblage just like playing with LEGO blocks, and orders of magnitude speedup can be obtained. The plug-and-play deformable model that will be the primary project outcome will advance state-of-the-art techniques in physical simulation, animation and visualization, and will also profoundly benefit a broad range of interdisciplinary fields that directly impact people in their daily lives, from the modeling and registration of deformable human organs for surgical simulation, to the analysis of roadway pavement stress, to silent speech recognition.The PI's approach pivots on the transformative concept of divide-and-conquer deformable model. Unlike most state-of-the-art techniques that simulate a deformable object in its entirely by means of a "one-stop" solver, the PI will develop innovative algorithms that break a simulation into independent computational modules, with the final result being obtained by incrementally assembling the local computations. The PI will seek theoretical solutions to two general questions: "how to smartly divide" and "how to effectively conquer" in the context of deformable simulation. In particular, he will investigates a theoretically grounded domain decomposition and coupling mechanism so that domain-level computation is independent, reusable, modularized and also a good fit with existing parallel computing architectures such as multi-core CPUs or GPUs. The PI will develop a new theory for the real-time spectral deformation processing that divides the simulation not only spatially but also spectrally, based on a power iteration and inertia analysis. He will also explore possible solutions to the problem of optimal domain partitioning, in which the simulation is parameterized geometrically and the most effective partition is obtained by solving a geometry optimization problem similar to the Voronoi diagram. As the test-bed for the aforementioned theoretical and algorithmic advances, the PI will develop a haptic-enabled collaborative digital fabrication system, which will ultimately allow multiple users, from distant sites to smoothly interact to design and craft physically simulated virtual objects, which can then be 3D printed if desired.

数据采集​​工具的进步导致3D数据的几何复杂性急剧提高。 有效地建模，模拟和分析这些扫描的大规模现实世界模型成为一个严重的挑战，因为高维部分差分方程（数百万自由度）的数值整合对于诸如手术模拟，生物模拟，虚拟/虚拟成像的现实和物理基础的动画和物理基础的动画和物理性的动画和物理性动画和物理性动画和物理性的动画和物理性的动画和物质上的时间限制性应用是过时的。 在经常改变3D模型的剩余几何形状的情况下，问题变得更加急剧，并且需要碰撞检测/响应，再加上异质材料属性的高忠诚度可视化以及在网络上有效传播的高忠诚度可视化以促进协作互动。 在该项目中，PI将通过制定研究计划来解决这一挑战，以创建一个模块化的计算框架，以通过将变形的身体划分为小型域，并使用虚弱的链接将它们重新连接回到小型域，从而创建一个模块化的计算框架。 域级计算是独立的和可重复的。因此，昂贵的可变形仿真被重新构建为插件的计算组合，就像使用乐高积木一样，并且可以获得数量级的加速顺序。 将成为主要项目结果的插件可变形模型将推进物理模拟，动画和可视化的最新技术，并且还将深刻地使广泛的跨学科领域受益，这些领域直接影响人们在日常生活中的人们，从可变形的人类内脏的模拟和注册中，以对路线的概念进行不断变形的态度，以分析态度的态度。分裂和诱使变形模型。 与大多数最先进的技术通过完全通过“一站式”求解器模拟变形对象的最先进的技术不同，PI将开发创新的算法，这些算法将模拟分解为独立的计算模式，并通过逐步组装局部计算而获得最终结果。 PI将向两个一般问题寻求理论解决方案：在可变形模拟的背景下，“如何巧妙地分裂”和“如何有效征服”。 特别是，他将研究理论上扎根的域分解和耦合机制，以便域级计算是独立的，可重复使用的，模块化的，并且与现有的平行计算体系结构（如多核CPU或GPU）非常吻合。 PI将开发一种新的理论，用于实时光谱变形处理，该理论不仅在空间上，而且基于频谱，基于功率迭代和惯性分析。 他还将探索解决最佳域分区问题的可能解决方案，其中模拟是几何被参数化的，并且通过求解类似于Voronoi图的几何优化问题来获得最有效的分区。 作为上述理论和算法进步的测试床，PI将开发一个具有触觉的协作数字制造系统，该系统最终将允许多个用户，从遥远的站点来平稳交互，以设计和制作物理模拟的虚拟对象，如果需要进行3D打印，则可以进行3D打印。