Subspace fluid re-simulation

Kim, Theodore; Delaney, John S.

doi:10.1145/2461912.2461987

Cited by 53 publications

(43 citation statements)

References 65 publications

(80 reference statements)

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“…The cubature approach has been successfully applied to a wide variety of non-linearities, including several non-linear material models , and the quadratic term in the inviscid Euler equations [Kim and Delaney 2013]. In our current work, we have found that it can be applied to the material model of interest [McAdams et al 2011], and more importantly, to self-collisions.…”

Section: Simulation Preliminariesmentioning

confidence: 90%

“…When such a tensor is not available, the cubature approach introduced by An et al [2008] can be applied, as it only requires a method of point-sampling the non-linearity. This approach was successfully applied to fluids [Kim and Delaney 2013] and used to make subspace methods more resilient to external collisions [Harmon and Zorin 2013]. The cubature training stage can be timeconsuming, so efficient methods such as importance sampling [Kim and Delaney 2013;Harmon and Zorin 2013] and Hard Thresholding Pursuit (HTP) [von Tycowicz et al 2013] have been developed.…”

Section: Related Workmentioning

confidence: 99%

“…Promising candidates for C can be located in a variety of ways, including a greedy search , importance sampling [Kim and Delaney 2013;Zorin 2013], or HTP [von Tycowicz et al 2013]. We used importance sampling in this work.…”

Section: A Direct Cubature Schemementioning

confidence: 99%

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Simulating articulated subspace self-contact

Teng

Otaduy²,

Kim

2014

ACM Trans. Graph.

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Figure 1: A hand mesh composed of 458K tetrahedra, running at 5.8 FPS (171 ms), including both self-contact detection and resolution. Our algorithm accelerates the computation of complex self-contacts by a factor of 5× to 52× over other subspace methods and 166× to 391× over full-rank simulations. Our self-contact computation never dominates the total time, and takes up at most 46% of a single frame. AbstractWe present an efficient new subspace method for simulating the self-contact of articulated deformable bodies, such as characters. Self-contact is highly structured in this setting, as the limited space of possible articulations produces a predictable set of coherent collisions. Subspace methods can leverage this coherence, and have been used in the past to accelerate the collision detection stage of contact simulation. We show that these methods can be used to accelerate the entire contact computation, and allow self-contact to be resolved without looking at all of the contact points. Our analysis of the problem yields a broader insight into the types of nonlinearities that subspace methods can efficiently approximate, and leads us to design a pose-space cubature scheme. Our algorithm accelerates self-contact by up to an order of magnitude over other subspace simulations, and accelerates the overall simulation by two orders of magnitude over full-rank simulations. We demonstrate the simulation of high resolution (100K -400K elements) meshes in self-contact at interactive rates (5.8 -50 FPS).

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Section: Simulation Preliminariesmentioning

confidence: 90%

Section: Related Workmentioning

confidence: 99%

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Simulating articulated subspace self-contact

Teng

Otaduy²,

Kim

2014

ACM Trans. Graph.

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“…This method was also used to reduce thin shell dynamics by Chadwick et al [2009], and can be extended to support online updating of the basis [Kim and James 2009] and domain decomposition [Kim and James 2011]. Kim et al [2013] also applied this technique to fluid simulation. Similar to our work, this work also model reduces inverse matrices and builds separate bases for each step of the dynamics.…”

Section: Related Workmentioning

confidence: 99%

Non-polynomial Galerkin projection on deforming meshes

et al. 2013

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Figure 1: Our method enables reduced simulation of fluid flow around this flying bird over 2000 times faster than the corresponding full simulation and reduced radiosity computation in this architectural scene over 113 times faster than the corresponding full radiosity. AbstractThis paper extends Galerkin projection to a large class of nonpolynomial functions typically encountered in graphics. We demonstrate the broad applicability of our approach by applying it to two strikingly different problems: fluid simulation and radiosity rendering, both using deforming meshes. Standard Galerkin projection cannot efficiently approximate these phenomena. Our approach, by contrast, enables the compact representation and approximation of these complex non-polynomial systems, including quotients and roots of polynomials. We rely on representing each function to be model-reduced as a composition of tensor products, matrix inversions, and matrix roots. Once a function has been represented in this form, it can be easily model-reduced, and its reduced form can be evaluated with time and memory costs dependent only on the dimension of the reduced space.

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“…For simulations involving moving solids, model reduction can also be conducted on a moving grid [Cohen et al 2010]. The use of cubature, initially proposed to achieve model-reduced simulation of elastic models von Tycowicz et al 2013;Li et al 2014], can speed up re-simulation of fluids in a reduced subspace as well [Kim and Delaney 2013]. However, the gain in efficiency of all such model-reduced simulations is often counterbalanced by (at times severe) energy or vorticity dissipation and the need for unstructured meshes to capture complex boundaries.…”

Section: Introductionmentioning

confidence: 99%

Model-reduced variational fluid simulation

Liu¹,

Mason

Hodgson

et al. 2015

ACM Trans. Graph.

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We present a model-reduced variational Eulerian integrator for incompressible fluids, which combines the efficiency gains of dimension reduction, the qualitative robustness of coarse spatial and temporal resolutions of geometric integrators, and the simplicity of sub-grid accurate boundary conditions on regular grids to deal with arbitrarily-shaped domains. At the core of our contributions is a functional map approach to fluid simulation for which scalar-and vector-valued eigenfunctions of the Laplacian operator can be easily used as reduced bases. Using a variational integrator in time to preserve liveliness and a simple, yet accurate embedding of the fluid domain onto a Cartesian grid, our model-reduced fluid simulator can achieve realistic animations in significantly less computational time than full-scale non-dissipative methods but without the numerical viscosity from which current reduced methods suffer. We also demonstrate the versatility of our approach by showing how it easily extends to magnetohydrodynamics and turbulence modeling in 2D, 3D and curved domains.

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Subspace fluid re-simulation

Cited by 53 publications

References 65 publications

Simulating articulated subspace self-contact

Simulating articulated subspace self-contact

Non-polynomial Galerkin projection on deforming meshes

Model-reduced variational fluid simulation

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