Abstract In this paper, we present a novel network‐based approach for reconstructing signed distance functions from fluid particles. The method uses a weighting kernel to transfer particles to a regular grid, which forms the input to a convolutional neural network. We propose a regression‐based regularization to reduce surface noise without penalizing high‐curvature features. The reconstruction exhibits improved spatial surface smoothness and temporal coherence compared with existing state of the art surface reconstruction methods. The method is insensitive to particle sampling density and robustly handles thin features, isolated particles, and sharp edges.

Abstract Micro‐macro models provide a powerful tool to study the relationship between microscale mechanisms and emergent macroscopic behavior. However, the detailed microscopic modeling requires tracking and evolving a potentially high‐dimensional configuration space at high computational cost. In this work, we present a novel parallel algorithm for simulating a high‐dimensional micro‐macro model of a gliding motility assay. We utilize a holistic approach aligning the data residency and simulation scales with the hybrid CPU and multi‐GPU hardware. Our novel approach achieves a speedup factor of 9.25× over previous GPU‐accelerated micro‐macro methods on the same hardware. Furthermore, by decoupling dependencies in the microstructure update, we are able to efficiently distribute the microstructure over multiple GPUs with minimal overhead. We test on up to four GPUs and observe excellent scaling, suggesting that significant further speedups are achievable with additional GPUs. Our approach enables micro‐macro simulations of higher complexity and resolution than would otherwise be feasible.

Abstract Time steps for explicit MPM simulation in computer graphics are often selected by trial and error due to the challenges in automatically selecting stable time step sizes. Our time integration scheme uses time step restrictions that take into account forces, collisions, and even grid‐to‐particle transfers calculated near the end of the time step. We propose a novel set of time step restrictions that allow a time step to be selected that is stable, efficient to compute, and not too far from optimal. We derive the general solution for the sound speed in nonlinear isotropic hyperelastic materials, which we use to enforce the classical CFL time step restriction. We identify a single‐particle instability in explicit MPM integration and propose a corresponding time step restriction in the fluid case. We also propose a reflection‐based boundary condition for domain walls that supports separation and accurate Coulomb friction while preventing particles from penetrating the domain walls.

We present a novel extended partitioned method for two-way solid-fluid coupling, where the fluid and solid solvers are treated as black boxes with limited exposed interfaces, facilitating modularity and code reusability. Our method achieves improved stability and extended range of applicability over standard partitioned approaches through three techniques. First, we couple the black-box solvers through a small, reduced-order monolithic system, which is constructed on the fly from input/output pairs generated by the solid and fluid solvers. Second, we use a conservative, impulse-based interaction term to couple the solid and fluid rather than typical pressure-based forces. We show that both of these techniques significantly improve stability and reduce the number of iterations needed for convergence. Finally, we propose a novel boundary pressure projection method that allows for the partitioned simulation of a fully enclosed fluid coupled to a dynamic solid, a scenario that has been problematic for partitioned methods. We demonstrate the benefits of our extended partitioned method by coupling Eulerian fluid solvers for smoke and water to Lagrangian solid solvers for volumetric and thin deformable and rigid objects in a variety of challenging scenarios. We further demonstrate our method by coupling a Lagrangian SPH fluid solver to a rigid body solver.

In this paper, we revisit the problem online reclustering in clustered shape matching simulations and propose an approach that employs two nonlinear optimizations to create new clusters. The first optimization finds the embedding of particles and clusters into three-dimensional space that minimizes elastic energy. The second finds the optimal location for the new cluster, working in this embedded space. The result is an approach that is more robust in the presence of elastic deformation. We also experimentally verify that our clustered shape matching approach converges as the number of clusters increases, suggesting that our reclustering approach does not change the underlying material properties. Further, we demonstrate that particle resampling is not strictly necessary in our framework allowing us to trivially conserve volume. Finally, we highlight an error in estimating rotations in the original shape-matching work [Müller et al. 2005] that has been repeated in much of the follow up work.

We introduce a new collision proxy for example-based deformable bodies. Specifically, we approximate the deforming geometry as a union of spheres. During pre-computation we perform a sphere packing on the input, undeformed geometry. Then, for each example pose, we move and resize the spheres to approximate the example. During runtime we blend together these positions and radii, using the same skinning weights we use for the geometry. We demonstrate the method on a car crash example, where we achieve an overall speedup of 5--20 times, depending on the resolution of the collision proxy geometry.

In this paper, we incorporate ductile fracture into the clustered shape matching simulation framework for deformable bodies, thus filling a gap in the shape matching literature. Our plasticity and fracture models are inspired by the finite element literature on deformable bodies, but are adapted to the clustered shape matching framework. The resulting approach is fast, versatile, and simple to implement.

Physics-based animation is often used to animate scenes containing destruction of near-rigid, man-made materials. For these applications, the most important visual features are plastic deformation and fracture. Methods based on continuum mechanics model these materials as elastoplastic, and must perform expensive elasticity computations even though elastic deformations are imperceptibly small for rigid materials. We introduce an example-based plasticity model based on linear blend skinning that allows artists to author simulation objects using familiar tools. Dynamics are computed using an unmodified rigid body simulator, making our method computationally efficient and easy to integrate into existing pipelines. We introduce a flexible technique for mapping impulses computed by the rigid body solver to local, example-based deformations. For completeness, our method also supports prescoring based fracture. We demonstrate the practicality of our method by animating a variety of destructive scenes.

In this paper, we address clustering and collision detection in the clustered shape matching simulation framework for deformable bodies. Our clustering algorithm is "fuzzy," meaning that it gives particles weighted membership in clusters. These weights are a significant extension to the basic clustered shape matching framework as they are used to divide particle mass among the clusters. We explore several weighting schemes and demonstrate that the choice of weighting scheme gives artists additional control over material behavior. Furthermore, by design our clustering algorithm yields spherical clusters, which not only results in sparse weight vectors, but also exceptionally efficient collision geometry. We further enhance this simple collision proxy by intersecting with half-spaces to allow for even better, yet still simple and computationally efficient, collision proxies. The resulting approach is fast, versatile, and simple to implement.

We propose a novel solid/fluid coupling method that treats the coupled system in a fully implicit manner making it stable for arbitrary time steps, large density ratios, etc. In contrast to previous work in computer graphics, we derive our method using a simple back-of-the-envelope approach which lumps the solid and fluid momenta together, and which we show exactly conserves the momentum of the coupled system. Notably, our method uses the standard Cartesian fluid discretization and does not require (moving) conforming tetrahedral meshes or ALE frameworks. Furthermore, we use a standard Lagrangian framework for the solid, thus supporting arbitrary solid constitutive models, both implicit and explicit time integration, etc. The method is quite general, working for smoke, water, and multiphase fluids as well as both rigid and deformable solids, and both volumes and thin shells. Rigid shells and cloth are handled automatically without special treatment, and we support fully one-sided discretizations without leaking. Our equations are fully symmetric, allowing for the use of fast solvers, which is a natural result of properly conserving momentum. Finally, for simple explicit time integration of rigid bodies, we show that our equations reduce to form similar to previous work via a single block Gaussian elimination operation, but that this approach scales poorly, i.e. as though four spatial dimensions rather than three.

We model flames and fire using the Navier-Stokes equations combined with the level set method and jump conditions to model the reaction front. Previous works modeled the flame using a combination of propagation in the normal direction and a curvature term which leads to a level set equation that is parabolic in nature and thus overly dissipative and smooth. Asymptotic theory shows that one can obtain more interesting velocities and fully hyperbolic (as opposed to parabolic) equations for the level set evolution. In particular, researchers in the field of detonation shock dynamics (DSD) have derived a set of equations which exhibit characteristic cellular patterns. We show how to make use of the DSD framework in the context of computer graphics simulations of flames and fire to obtain interesting features such as flame wrinkling and cellular patterns.

The particle level set method has proven successful for the simulation oftwoseparate regions (such as water and air, or fuel and products). In this paper, we propose a novel approach to extend this method to the simulation of as many regions as desired. The various regions can be liquids (or gases) of any type with differing viscosities, densities, viscoelastic properties, etc. We also propose techniques for simulating interactions between materials, whether it be simple surface tension forces or more complex chemical reactions with one material converting to another or two materials combining to form a third. We use a separate particle level set method for each region, and propose a novel projection algorithm that decodes the resulting vector of level set values providing a "dictionary" that translates between them and the standard single-valued level set representation. An additional difficulty occurs since discretization stencils (for interpolation, tracing semi-Lagrangian rays, etc.) cross region boundaries naively combining non-smooth or even discontinuous data. This has recently been addressed via ghost values, e.g. for fire or bubbles. We instead propose a new paradigm that allows one to incorporate physical jump conditions in data "on the fly," which is significantly more efficient for multiple regions especially at triple points or near boundaries with solids.