Category: Deformables

Fast Corotated FEM using Operator Splitting

Tassilo Kugelstadt, Dan Koschier, Jan Bender

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss-Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.

Fast Corotated FEM using Operator Splitting

An Extended Partitioned Method for Conservative Solid-Fluid Coupling

Muzaffer Akbay, Nicholas Nobles, Victor Zoran, Tamar Shinar

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

An Extended Partitioned Method for Conservative Solid-Fluid Coupling

Projective peridynamics for modeling versatile elastoplastic materials

Xiaowei He, Huamin Wang, Enhua Wu

Unified simulation of versatile elastoplastic materials and different dimensions offers many advantages in animation production, contact handling, and hardware acceleration. The unstructured particle representation is particularly suitable for this task, thanks to its simplicity. However, previous meshless techniques either need too much computational cost for addressing stability issues, or lack physical meanings and fail to generate interesting deformation behaviors, such as the Poisson effect. In this paper, we study the development of an elastoplastic model under the state-based peridynamics framework, which uses integrals rather than partial derivatives in its formulation. To model elasticity, we propose a unique constitutive model and an efficient iterative simulator solved in a projective dynamics way. To handle plastic behaviors, we incorporate our simulator with the Drucker-Prager yield criterion and a reference position update scheme, both of which are implemented under peridynamics. Finally, we show how to strengthen the simulator by position-based constraints and spatially varying stiffness models, to achieve incompressibility, particle redistribution, cohesion, and friction effects in viscoelastic and granular flows. Our experiments demonstrate that our unified, meshless simulator is flexible, efficient, robust, and friendly with parallel computing.

Projective peridynamics for modeling versatile elastoplastic materials

A Temporally Adaptive Material Point Method with Regional Time Stepping

Yu Fang, Yuanming Hu, Shi-Min Hu, Chenfanfu Jiang

Spatially and temporally adaptive algorithms can substantially improve the computational efficiency of many numerical schemes in computational mechanics and physics-based animation. Recently, a crucial need for temporal adaptivity in the Material Point Method (MPM) is emerging due to the potentially substantial variation of material stiffness and velocities in multi-material scenes. In this work, we propose a novel temporally adaptive symplectic Euler scheme for MPM with regional time stepping (RTS), where different time steps are used in different regions. We design a time stepping scheduler operating at the granularity of small blocks to maintain a natural consistency with the hybrid particle/grid nature of MPM. Our method utilizes the Sparse Paged Grid (SPGrid) data structure and simultaneously offers high efficiency and notable ease of implementation with a practical multi-threaded particle-grid transfer strategy. We demonstrate the efficacy of our asynchronous MPM method on various examples including elastic objects, granular media, and fluid.

A Temporally Adaptive Material Point Method with Regional Time Stepping

Time-Domain Parallelization for Accelerating Cloth Simulation

Junbang Liang, Ming C. Lin

Cloth simulations, widely used in computer animation and apparel design, can be computationally expensive for real-time applications. Some parallelization techniques have been proposed for visual simulation of cloth using CPU or GPU clusters and often rely on parallelization using spatial domain decomposition techniques that have a large communication overhead. In this paper, we propose a novel time-domain parallelization technique that makes use of the two-level mesh representation to resolve the time-dependency issue and develop a practical algorithm to smooth the state transition from the corresponding coarse to fine meshes. A load estimation and a load balancing technique used in online partitioning are also proposed to maximize the performance acceleration. Our method achieves a nearly linear performance scaling on manycore clusters and outperforms spatial-domain parallelization on a diverse set of benchmarks.

Time-Domain Parallelization for Accelerating Cloth Simulation

Hyper-Reduced Projective Dynamics

Christopher Brandt, Elmar Eisemann, Klaus Hildebrandt

We present a method for the real-time simulation of deformable objects that combines the robustness, generality, and high performance of Projective Dynamics with the efficiency and scalability offered by model reduction techniques. The method decouples the cost for time integration from the mesh resolution and can simulate large meshes in real-time. The proposed hyper-reduction of Projective Dynamics combines a novel fast approximation method for constraint projections and a scalable construction of sparse subspace bases. The resulting system achieves real-time rates for large subspaces enabling rich dynamics and can resolve general user interactions, collision constraints, external forces and changes to the materials. The construction of the hyper-reduced system does not require user-interaction and refrains from using training data or modal analysis, which results in a fast preprocessing stage.

Hyper-Reduced Projective Dynamics

Immersion of Self-Intersecting Solids and Surfaces

Yijing Li, Jernej Barbič

Self-intersecting, or nearly self-intersecting, meshes are commonly found in 2D and 3D computer graphics practice. Self-intersections occur, for example, in the process of artist manual work, as a by-product of procedural methods for mesh generation, or due to modeling errors introduced by scanning equipment. If the space bounded by such inputs is meshed naively, the resulting mesh joins (“glues”) self-overlapping parts, precluding efficient further modeling and animation of the underlying geometry. Similarly, near self-intersections force the simulation algorithm to employ an unnecessarily detailed mesh to separate the nearly self-intersecting regions. Our work addresses both of these challenges, by giving an algorithm to generate an “un-glued” simulation mesh, of arbitrary user-chosen resolution, that properly accounts for self-intersections and near self-intersections. In order to achieve this result, we study the mathematical concept of immersion, and give a deterministic and constructive algorithm to determine if the input self-intersecting triangle mesh is the boundary of an immersion. For near self-intersections, we give a robust algorithm to properly duplicate mesh elements and correctly embed the underlying geometry into the mesh element copies. Both the self-intersections and near self-intersections are combined into one algorithm that permits successful meshing at arbitrary resolution. Applications of our work include volumetric shape editing, physically based simulation and animation, and volumetric weight and geodesic distance computation on self-intersecting inputs.

Immersion of Self-Intersecting Solids and Surfaces

FEPR: Fast Energy Projection for Real-Time Simulation of Deformable Objects

Dimitar Dinev, Tiantian Liu, Jing Li, Bernhard Thomaszewski, Ladislav Kavan
We propose a novel projection scheme that corrects energy fluctuations in simulations of deformable objects, thereby removing unwanted numerical dissipation and numerical “explosions”. The key idea of our method is to first take a step using a conventional integrator, then project the result back to the constant energy-momentum manifold. We implement this strategy using fast projection, which only adds a small amount of overhead to existing physics-based solvers. We test our method with several implicit integration rules and demonstrate its benefits when used in conjunction with Position Based Dynamics and Projective Dynamics. When added to a dissipative integrator such as backward Euler, our method corrects the artificial damping and thus produces more vivid motion. Our projection scheme also effectively prevents
instabilities that can arise due to approximate solves or large time steps. Our method is fast, stable, and easy to implement—traits that make it well-suited for real-time physics applications such as games or training simulators.

FEPR: Fast Energy Projection for Real-Time Simulation of Deformable Objects

Anderson Acceleration for Geometry Optimization and Physics Simulation

Yue Peng, Bailin Deng, Juyong Zhang, Fanyu Geng, Wenjie Qin, Ligang liu

Many computer graphics problems require computing geometric shapes subject to certain constraints. This often results in non-linear and non-convex optimization problems with globally coupled variables, which pose great challenge for interactive applications. Local-global solvers developed in recent years can quickly compute an approximate solution to such problems, making them an attractive choice for applications that prioritize efficiency over accuracy. However, these solvers suffer from lower convergence rate, and may take a long time to compute an accurate result. In this paper, we propose a simple and effective technique to accelerate the convergence of such solvers. By treating each local-global step as a fixed-point iteration, we apply Anderson acceleration, a well-established technique for fixed-point solvers, to speed up the convergence of a local-global solver. To address the stability issue of classical Anderson acceleration, we propose a simple strategy to guarantee the decrease of target energy and ensure its global convergence. In addition, we analyze the connection between Anderson acceleration and quasi-Newton methods, and show that the canonical choice of its mixing parameter is suitable for accelerating local-global solvers. Moreover, our technique is effective beyond classical local-global solvers, and can be applied to iterative methods with a common structure. We evaluate the performance of our technique on a variety of geometry optimization and physics simulation problems. Our approach significantly reduces the number of iterations required to compute an accurate result, with only a slight increase of computational cost per iteration. Its simplicity and effectiveness makes it a promising tool for accelerating existing algorithms as well as designing efficient new algorithms.

Anderson Acceleration for Geometry Optimization and Physics Simulation

Projective Skinning

Martin Komaritzan, Mario Botsch

We present a novel approach for physics-based character skinning. While maintaining real-time performance it overcomes the well-known artifacts of commonly used geometric skinning approaches, it enables dynamic effects, and it resolves local self-collisions. Our method is based on a two-layer model consisting of rigid bones and an elastic soft tissue layer. This volumetric model is easily and efficiently computed from an input surface mesh of the character and its underlying skeleton. In particular, our method neither requires skinning weights, which are often expensive to compute or tedious to hand-tune, nor a complex volumetric tessellation, which fails for many real-world input meshes due to self-intersections.

Projective Skinning