CHS: Small: Towards Next-Generation Large-Scale Nonlinear Deformable Simulation

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Using a digital computer to accurately simulate soft objects that deform under external interactions is a fundamental problem in a wide range of scientific and engineering fields. For example, without being able to deliver a faithful force-displacement response, virtual surgical training is hardly effective and provides users with misleading experiences. In the past decade, the number of simulation degrees of freedom (DOFs) for deformable models has increased from hundreds to hundreds-of-thousands and even millions. Computing hardware that has become more and more powerful has contributed significantly to this development, but unfortunately it is unlikely that in the future computer simulation will continue to benefit dramatically from increased processor frequency. Indeed, in the last few years the chip industry has already moved the emphasis from a faster processor clock to multi-core architectures. On the other hand, with the widespread adoption of advanced acquisition devices/techniques, the complexity and scale of the data that can be handled by computers have grown exponentially, and large-scale geometries are becoming ubiquitous in modern 3D data processing. This new era of data explosion imposes unprecedented challenges on deformable simulation. Existing methods typically use one-stop solvers that calculate all the unknown DOFs of a system, but that is computationally intensive due to the underlying high-dimensional numerical integration. Even with state-of-the-art hardware, deformable simulation can still take hours, days, or even weeks for massive scenarios. Clearly, conventional simulation methodologies fail to well accommodate distributed computing resource allocation, and become more and more cumbersome with bigger and bigger datasets. This calls for rebranded algorithmic frameworks and dedicated numerical procedures for large-scale geometrically-complex and nonlinear deformable models that empower next-generation graphics applications. Motivated by these grand challenges, this project systematically investigates a collection of theoretical advancements, computational techniques, and numerical implementations that push the frontier of large-scale nonlinear deformable models to "post Moore's law." Specifically, the intellectual merit of the research will comprise the following aspects:o The project will devise a theoretically grounded domain decomposition based parallel deformable simulator. By weakening inter-domain linkages, the domain-level computations become independent and parallelizable. The coupling mechanism will be generalized and enriched so that non-conforming and overlapping domain decompositions are made possible. This includes an in-depth optimization of the domain tessellation under specified hardware configurations. Simulation reusability will be further enhanced through a novel technique called cellular domains.o The project will deepen the current understanding of large-scale model reduction and re-forge this useful tool in the context of parallel computing. In particular, how to utilize power iteration to obtain the spectral analysis will be explored. Furthermore, geometry-based reduction directly dictates reduced DOFs and has a more robust simulation even under imposed extreme constraints.o A well-argued computational theory is less practicable unless encapsulated by a set of carefully engineered implementations. Accordingly, the project will also design customized numerical procedures paired with proposed algorithmic techniques, and the entire simulation framework will be fine-tuned at the system level, solver level, and sub-solver level by leveraging unique data patterns, numerical behaviors, and problem structures of domain decomposed deformable models.o As a testbed platform, the project will develop a novel real-time human tongue motion visualization system. Over 8% of U.S. children have a communication or swallowing disorder. Built upon the new deformation solver, an ultrasound-imaging-driven real-time human tongue visualization system will be developed to assist doctors and speech therapists to better understand the pathological mechanism behind this disease and plan more effective subject-specific medical/physical treatments.