Decomposed optimization time integrator for large-step elastodynamics

Li, Minchen; Gao, Ming; Langlois, Timothy R.; Jiang, Chenfanfu; Kaufman, Danny M.

doi:10.1145/3306346.3322951

Cited by 38 publications

(12 citation statements)

References 37 publications

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“…We employed Bridson's collision detection and resolution strategy [Bridson et al 2002]. Time integration was performed with backward Euler; we solved the resulting nonlinear systems using a standard Newton solver with conjugate gradient for the inner linear solves, although it would be interest to explore alternatives for greater efficiency [Li et al 2019]. We did not observe any significant change in the stability using our method as compared to pure simulations of a particular dimension.…”

Section: Resultsmentioning

confidence: 98%

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Chang

Da²,

Grinspun

et al. 2019

Proc. ACM Comput. Graph. Interact. Tech.

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We present a unified method to simulate deformable elastic bodies consisting of mixed-dimensional components represented with potentially non-manifold simplicial meshes. Building on well-known simplicial rod, shell, and solid models for elastic continua, we categorize and define a comprehensive palette expressing all possible constraints and elastic energies for stiff and flexible connections between the 1D, 2D, and 3D components of a single conforming simplicial mesh. This palette consists of three categories: point connections, in which simplices meet at a single vertex around which they may twist and bend; curve connections in which simplices share an edge around which they may rotate (bend) relative to one another; and surface connections, in which a shell is embedded on or into a solid. To define elastic behaviors across non-manifold point connections, we adapt and apply parallel transport concepts from elastic rods. To address discontinuous forces that would otherwise arise when large accumulated relative rotations wrap around in the space of angles, we develop an incremental angle-update strategy. Our method provides a conceptually simple, flexible, and highly expressive framework for designing complex elastic objects, by modeling the geometry with a single simplicial mesh and decorating its elements with appropriate physical models (rod, shell, solid) and connection types (point, curve, surface). We demonstrate a diverse set of possible interactions achievable with our method, through technical and application examples, including scenes featuring complex aquatic creatures, children's toys, and umbrellas.

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Section: Resultsmentioning

confidence: 98%

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Chang

Da²,

Grinspun

et al. 2019

Proc. ACM Comput. Graph. Interact. Tech.

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“…Martin et al [MTGG11] show that the Backward Euler method can be formulated as an optimization problem. This enables to speed up computations by using efficient optimization methods like alternating local‐global solvers [LBBK13, BML ∗ 14], Newton's method with sophisticated line search strategies [GSS ∗ 15], the Chebyshev Semi‐Iterative approach [Wan15], ADMM [OBLN17], L‐BFGS [LBK17], or domain decomposition [LGL ∗ 19]. Moreover there are specialized material models which are well suited to be used with optimization integrators [KKB18].…”

Section: Related Workmentioning

confidence: 99%

Higher‐Order Time Integration for Deformable Solids

Löschner

Longva

Jeske

et al. 2020

Computer Graphics Forum

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Visually appealing and vivid simulations of deformable solids represent an important aspect of physically based computer animation. For the temporal discretization, it is customary in computer animation to use first‐order accurate integration methods, such as Backward Euler, due to their simplicity and robustness. Although there is notable research on second‐order methods, their use is not widespread. Many of these well‐known methods have significant drawbacks such as severe numerical damping or scene‐dependent time step restrictions to ensure stability. In this paper, we discuss the most relevant requirements on such methods in computer animation and motivate the interest beyond first‐order accuracy. Keeping these requirements in mind, we investigate several promising methods from the families of diagonally implicit Runge‐Kutta (DIRK) and Rosenbrock methods which currently do not appear to have considerable popularity in this field. We show that the usage of such methods improves the visual quality of physical animations. In addition, we demonstrate that they allow distinctly more control over damping at lower computational cost than classical methods. As part of our theoretical contribution, we review aspects of simulations that are often considered more intricate with higher‐order methods, such as contact handling. To this end, we derive an implicit linearized contact model based on a predictor‐corrector approach that leads to consistent behavior with higher‐order integrators as predictors. Our contact model is well suited for the simulation of stiff, nonlinear materials with the integration methods presented in this paper and more common methods such as Backward Euler alike.

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“…However details matter, and there are key differences between EMU and projective dynamics as highlighted in Table 1. Although one component of our energy term resembles the term in Projective Dynamics, rather than minimize this energy using alternating projections or a variant of the alternating direction method of multipliers [NOB16], we leverage the algebraic properties of this energy to construct an efficient quasi‐newton algorithm [WN99] with capabilities beyond the quasi‐newton algorithms proposed in [LBK17, ZBK18, LGL*19].…”

Section: Related Workmentioning

confidence: 99%

EMU: Efficient Muscle Simulation in Deformation Space

Modi

Fulton

Jacobson

et al. 2020

Computer Graphics Forum

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EMU is an efficient and scalable model to simulate bulk musculoskeletal motion with heterogenous materials. First, EMU requires no model reductions, or geometric coarsening, thereby producing results visually accurate when compared to an FEM simulation. Second, EMU is efficient and scales much better than state‐of‐the‐art FEM with the number of elements in the mesh, and is more easily parallelizable. Third, EMU can handle heterogeneously stiff meshes with an arbitrary constitutive model, thus allowing it to simulate soft muscles, stiff tendons and even stiffer bones all within one unified system. These three key characteristics of EMU enable us to efficiently orchestrate muscle activated skeletal movements. We demonstrate the efficacy of our approach via a number of examples with tendons, muscles, bones and joints.

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Decomposed optimization time integrator for large-step elastodynamics

Cited by 38 publications

References 37 publications

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

A Unified Simplicial Model for Mixed-Dimensional and Non-Manifold Deformable Elastic Objects

Higher‐Order Time Integration for Deformable Solids

EMU: Efficient Muscle Simulation in Deformation Space

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