37-Issue 8

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https://diglib.eg.org/handle/10.2312/2632544

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Browsing 37-Issue 8 by Subject "Computer graphics"

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    Cosserat Rods with Projective Dynamics
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Soler, Carlota; Martin, Tobias; Sorkine-Hornung, Olga; Thuerey, Nils and Beeler, Thabo
    We present a novel method to simulate Cosserat rods with Projective Dynamics (PD). The proposed method is both numerically robust and accurate with respect to the underlying physics, making it suitable for a variety of applications in computer graphics and related disciplines. Cosserat theory assigns an orientation frame to each point and is thus able to realistically simulate stretching and shearing effects, in addition to bending and twisting. Within the PD framework, it is possible to obtain accurate simulations given the implicit integration over time and its decoupling of the local-global solve. In the proposed method, we start from the continuous formulation of the Cosserat theory and derive the constraints for the PD solver.We extend the standard definition of PD and add body orientations as system variables. Thus, we include the preservation of angular momentum, so that twisting and bending can be accurately simulated. Our formulation allows the simulation of different bending behaviors with respect to a user-defined Young's modulus, the radius of the rod's cross-section, and material density. We show how different material specifications in our simulations converge within a few iterations to a reference solution, generated with a highprecision finite element method. Furthermore, we demonstrate mesh independence of our formulation: Refining the simulation mesh still results in the same characteristic motion, which is in contrast to previous position based methods.
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    Distributing and Load Balancing Sparse Fluid Simulations
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Shah, Chinmayee; Hyde, David; Qu, Hang; Levis, Philip; Thuerey, Nils and Beeler, Thabo
    This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a speculative low resolution simulation in parallel. We mathematically formulate the problem of load balancing over multiple time steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.3 to 7.9, and that speculative load balancing generates assignments that perform within 20% of optimal.
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    An Efficient Solver for Two-way Coupling Rigid Bodies with Incompressible Flow
    (The Eurographics Association and John Wiley & Sons Ltd., 2018) Aanjaneya, Mridul; Thuerey, Nils and Beeler, Thabo
    We present an efficient solver for monolithic two-way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low-dimensional nature of the solid equations. We observe that a single Multigrid V-cycle for the fluid equations serves as a very effective preconditioner for solving the Schur-complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly-free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two-way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation.