Hierarchical Optimization Time Integration for CFL-rate MPM Stepping

We propose Hierarchical Optimization Time Integration (HOT) for efficient implicit time-stepping of the Material Point Method (MPM) irrespective of simulated materials and conditions. HOT is an MPM-specialized hierarchical optimization algorithm that solves nonlinear time step problems for large-scale MPM systems near the CFL-limit. HOT provides convergent simulations "out-of-the-box" across widely varying materials and computational resolutions without parameter tuning. As an implicit MPM time stepper accelerated by a custom-designed Galerkin multigrid wrapped in a quasi-Newton solver, HOT is both highly parallelizable and robustly convergent. As we show in our analysis, HOT maintains consistent and efficient performance even as we grow stiffness, increase deformation, and vary materials over a wide range of finite strain, elastodynamic and plastic examples. Through careful benchmark ablation studies, we compare the effectiveness of HOT against seemingly plausible alternative combinations of MPM with standard multigrid and other Newton-Krylov models. We show how these alternative designs result in severe issues and poor performance. In contrast, HOT outperforms the existing state-of-the-art, heavily optimized implicit MPM codes with an up to 10x performance speedup across a wide range of challenging benchmark test simulations

Soft Hybrid Aerial Vehicle via Bistable Mechanism

Unmanned aerial vehicles have been demonstrated successfully in a variety of tasks, including surveying and sampling tasks over large areas. These vehicles can take many forms. Quadrotors' agility and ability to hover makes them well suited for navigating potentially tight spaces, while fixed wing aircraft are capable of efficient flight over long distances. Hybrid aerial vehicles (HAVs) attempt to achieve both of these benefits by exhibiting multiple modes; however, morphing HAVs typically require extra actuators which add mass, reducing both agility and efficiency. We propose a morphing HAV with folding wings that exhibits both a quadrotor and a fixed wing mode without requiring any extra actuation. This is achieved by leveraging the motion of a bistable mechanism at the center of the aircraft to drive folding of the wing using only the existing motors and the inertia of the system. We optimize both the bistable mechanism and the folding wing using a topology optimization approach. The resulting mechanisms were fabricated on a 3D printer and attached to an existing quadrotor frame. Our prototype successfully transitions between both modes and our experiments demonstrate that the behavior of the fabricated prototype is consistent with that of the simulation.Comment: 7 pages, 10 figure

P-Cloth: Interactive Complex Cloth Simulation on Multi-GPU Systems using Dynamic Matrix Assembly and Pipelined Implicit Integrators

We present a novel parallel algorithm for cloth simulation that exploits multiple GPUs for fast computation and the handling of very high resolution meshes. To accelerate implicit integration, we describe new parallel algorithms for sparse matrix-vector multiplication (SpMV) and for dynamic matrix assembly on a multi-GPU workstation. Our algorithms use a novel work queue generation scheme for a fat-tree GPU interconnect topology. Furthermore, we present a novel collision handling scheme that uses spatial hashing for discrete and continuous collision detection along with a non-linear impact zone solver. Our parallel schemes can distribute the computation and storage overhead among multiple GPUs and enable us to perform almost interactive simulation on complex cloth meshes, which can hardly be handled on a single GPU due to memory limitations. We have evaluated the performance with two multi-GPU workstations (with 4 and 8 GPUs, respectively) on cloth meshes with 0.5-1.65M triangles. Our approach can reliably handle the collisions and generate vivid wrinkles and folds at 2-5 fps, which is significantly faster than prior cloth simulation systems. We observe almost linear speedups with respect to the number of GPUs

Codimensional Incremental Potential Contact

We extend the incremental potential contact (IPC) model [Li et al. 2020a] for contacting elastodynamics to resolve systems composed of arbitrary combinations of codimensional degrees-of-freedoms. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending the IPC model to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend IPC to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (mid-lines) of shells (rods) will not move closer than applied thickness values, even as these thicknesses become characteristically small. This enables us to account for thickness in the contact behavior of codimensional structures and so robustly capture challenging contacting geometries; a number of which, to our knowledge, have not been simulated before. Third, codimensional models, especially with modeled thickness, mandate strict accuracy requirements that pose a severe challenge to all existing continuous collision detection (CCD) methods. To address these limitations we develop a new, efficient, simple-to-implement additive CCD (ACCD) method that iteratively refines a lower bound converging to time of impact