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

数据采集工具的进步导致了三维数据几何复杂性的急剧增加。有效地建模、模拟和分析这些扫描的大规模真实世界模型成为一项严峻的挑战，因为高维偏微分方程（超过数百万个自由度）的数值积分对于时间关键应用（如外科模拟、生物医学成像、虚拟/增强现实和基于物理的动画）是令人生畏的。在3D模型的静态几何形状经常改变的情况下，这个问题变得更加严重，需要碰撞检测/响应，以及异质材料特性的高保真可视化和通过网络的有效传输，以促进协作交互。在这个项目中，PI将通过开发一个研究项目来解决这一挑战，通过将可变形体划分为小尺寸域并使用弱连接将它们重新连接起来，创建一个模块化的计算框架，用于有效的可变形模拟。领域级计算具有独立性和可重用性；因此，昂贵的可变形模拟被重新定义为一个即插即用的计算组合，就像玩乐高积木一样，并且可以获得数量级的加速。即插即用的可变形模型将是主要的项目成果，它将推动物理模拟、动画和可视化方面的最先进技术，并将深刻地受益于直接影响人们日常生活的广泛跨学科领域，从用于外科模拟的可变形人体器官的建模和注册，到道路路面应力分析，再到无声语音识别。PI的方法以分而治之的可变形模型的变革概念为中心。与大多数最先进的技术完全通过“一站式”求解器模拟可变形物体不同，PI将开发创新的算法，将模拟分解为独立的计算模块，最终结果通过增量组装局部计算获得。PI将在可变形模拟的背景下寻求两个一般问题的理论解决方案：“如何巧妙地划分”和“如何有效地征服”。特别是，他将研究一个理论基础的领域分解和耦合机制，使领域级计算是独立的，可重用的，模块化的，也很好地适应现有的并行计算架构，如多核cpu或gpu。PI将基于功率迭代和惯性分析，为实时频谱变形处理开发一种新的理论，该理论不仅在空间上而且在频谱上划分模拟。他还将探索最优域划分问题的可能解决方案，其中模拟是几何参数化的，通过解决类似于Voronoi图的几何优化问题来获得最有效的划分。作为上述理论和算法进步的试验台，PI将开发一个触觉支持的协作数字制造系统，最终允许多个用户从遥远的地点顺利交互，设计和制作物理模拟的虚拟物体，然后可以根据需要进行3D打印。

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.