29 results on '"Aanjaneya, Mridul"'
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2. On a generalized energy conservation/dissipation time finite element method for Hamiltonian mechanics
- Author
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Xue, Tao, Wang, Yazhou, Aanjaneya, Mridul, Tamma, Kumar K., and Qin, Guoliang
- Published
- 2021
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3. A Closest Point Method for Surface PDEs with Interior Boundary Conditions for Geometry Processing
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King, Nathan, Su, Haozhe, Aanjaneya, Mridul, Ruuth, Steven, and Batty, Christopher
- Subjects
FOS: Computer and information sciences ,Computer Science - Graphics ,Graphics (cs.GR) - Abstract
Many geometry processing techniques require the solution of partial differential equations (PDEs) on surfaces. Such surface PDEs often involve boundary conditions prescribed on the surface, at points or curves on its interior or along the geometric (exterior) boundary of an open surface. However, input surfaces can take many forms (e.g., meshes, parametric surfaces, point clouds, level sets, neural implicits). One must therefore generate a mesh to apply finite element-type techniques or derive specialized discretization procedures for each surface representation. We propose instead to address such problems through a novel extension of the closest point method (CPM) to handle interior boundary conditions specified at surface points or curves. CPM solves the surface PDE by solving a volumetric PDE defined over the Cartesian embedding space containing the surface; only a closest point function is required to represent the surface. As such, CPM supports surfaces that are open or closed, orientable or not, and of any codimension or even mixed-codimension. To enable support for interior boundary conditions, we develop a method to implicitly partition the embedding space across interior boundaries. CPM's finite difference and interpolation stencils are adapted to respect this partition while preserving second-order accuracy. Furthermore, an efficient sparse-grid implementation and numerical solver is developed that can scale to tens of millions of degrees of freedom, allowing PDEs to be solved on more complex surfaces. We demonstrate our method's convergence behaviour on selected model PDEs. Several geometry processing problems are explored: diffusion curves on surfaces, geodesic distance, tangent vector field design, and harmonic map construction. Our proposed approach thus offers a powerful and flexible new tool for a range of geometry processing tasks on general surface representations., 24 pages
- Published
- 2023
4. Towards positivity preservation for monolithic two-way solid–fluid coupling
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Patkar, Saket, Aanjaneya, Mridul, Lu, Wenlong, Lentine, Michael, and Fedkiw, Ronald
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- 2016
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5. A monolithic mass tracking formulation for bubbles in incompressible flow
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Aanjaneya, Mridul, Patkar, Saket, and Fedkiw, Ronald
- Published
- 2013
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6. Diffuse reflection diameter and radius for convex-quadrilateralizable polygons
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Khan, Arindam, Pal, Sudebkumar P., Aanjaneya, Mridul, Bishnu, Arijit, and Nandy, Subhas C.
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- 2013
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7. An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids.
- Author
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Cao, Yadi, Chen, Yunuo, Li, Minchen, Yang, Yin, Zhang, Xinxin, Aanjaneya, Mridul, and Jiang, Chenfanfu
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COMPRESSIBLE flow ,FRACTURE mechanics ,SHOCK waves ,MATERIAL point method ,THEORY of wave motion - Abstract
This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured. [ABSTRACT FROM AUTHOR]
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- 2022
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8. Tromino tilings of domino-deficient rectangles
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Aanjaneya, Mridul
- Published
- 2009
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9. Spring-Rod System Identification via Differentiable Physics Engine
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Wang, Kun, Aanjaneya, Mridul, and Bekris, Kostas
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FOS: Computer and information sciences ,Computer Science - Robotics ,Computer Science - Machine Learning ,Artificial Intelligence (cs.AI) ,Computer Science - Graphics ,Computer Science - Artificial Intelligence ,Robotics (cs.RO) ,Graphics (cs.GR) ,Machine Learning (cs.LG) - Abstract
We propose a novel differentiable physics engine for system identification of complex spring-rod assemblies. Unlike black-box data-driven methods for learning the evolution of a dynamical system \emph{and} its parameters, we modularize the design of our engine using a discrete form of the governing equations of motion, similar to a traditional physics engine. We further reduce the dimension from 3D to 1D for each module, which allows efficient learning of system parameters using linear regression. The regression parameters correspond to physical quantities, such as spring stiffness or the mass of the rod, making the pipeline explainable. The approach significantly reduces the amount of training data required, and also avoids iterative identification of data sampling and model training. We compare the performance of the proposed engine with previous solutions, and demonstrate its efficacy on tensegrity systems, such as NASA's icosahedron., Workshop on Differentiable Vision, Graphics, and Physics in Machine Learning at NeurIPS 2020. arXiv admin note: substantial text overlap with arXiv:2004.13859
- Published
- 2020
10. A‐ULMPM: An Adaptively Updated Lagrangian Material Point Method for Efficient Physics Simulation without Numerical Fracture.
- Author
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Su, Haozhe, Xue, Tao, Han, Chengguizi, and Aanjaneya, Mridul
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MATERIAL point method ,LAGRANGIAN points ,PHYSICS ,VISCOUS flow ,EULERIAN graphs - Abstract
We present an adaptively updated Lagrangian Material Point Method (A‐ULMPM) to alleviate non‐physical artifacts, such as the cell‐crossing instability and numerical fracture, that plague state‐of‐the‐art Eulerian formulations of MPM, while still allowing for large deformations that arise in fluid simulations. A‐ULMPM spans MPM discretizations from total Lagrangian formulations to Eulerian formulations. We design an easy‐to‐implement physics‐based criterion that allows A‐ULMPM to update the reference configuration adaptively for measuring physical states, including stress, strain, interpolation kernels and their derivatives. For better efficiency and conservation of angular momentum, we further integrate the APIC [JSS*15] and MLS‐MPM [HFG*18] formulations in A‐ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first‐order derivatives. Our theoretical derivations use a nodal discretized Lagrangian, instead of the weak form discretization in MLS‐MPM [HFG*!!18], and naturally lead to a "modified" MLS‐MPM in A‐ULMPM, which can recover MLS‐MPM using a completely Eulerian formulation. A‐ULMPM does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes. We present end‐to‐end 3D simulations of stretching and twisting hyperelastic solids, viscous flows, splashing liquids, and multi‐material interactions with large deformations to demonstrate the efficacy of our new method. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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11. A novel approach to generate correctly rounded math libraries for new floating point representations
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Aanjaneya, Mridul, Gustafson, John, Nagarakatte, Santosh, and Lim, Jay
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FOS: Computer and information sciences ,Elementary functions ,Computer Science - Mathematical Software ,Mathematical Software (cs.MS) ,Floating point ,Math libraries ,Correctly rounded result - Abstract
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded math libraries. Further, the use of existing FP libraries for these new representations can produce incorrect results. This paper proposes a novel approach for generating polynomial approximations that can be used to implement correctly rounded math libraries. Existing methods generate polynomials that approximate the real value of an elementary function $f(x)$ and produce wrong results due to approximation errors and rounding errors in the implementation. In contrast, our approach generates polynomials that approximate the correctly rounded value of $f(x)$ (i.e., the value of $f(x)$ rounded to the target representation). It provides more margin to identify efficient polynomials that produce correctly rounded results for all inputs. We frame the problem of generating efficient polynomials that produce correctly rounded results as a linear programming problem. Our approach guarantees that we produce the correct result even with range reduction techniques. Using our approach, we have developed correctly rounded, yet faster, implementations of elementary functions for multiple target representations., 44 pages
- Published
- 2020
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12. A Lagrangian Particle‐based Formulation for Coupled Simulation of Fracture and Diffusion in Thin Membranes.
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Han, Chengguizi, Xue, Tao, and Aanjaneya, Mridul
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ALUMINUM foil ,WRINKLE patterns ,COMPUTER graphics ,DIFFUSION processes - Abstract
We propose a Lagrangian particle‐based formulation for simulating deformation, fracture, and diffusion in thin membranelike structures, such as aluminium foil, rubbery films, and seaweed flakes. We integrate our model with diffusion processes and derive a unified framework for simulating deformation‐diffusion coupled phenomena, which is applied to provide realistic heterogeneity induced by the diffusion process to fracture patterns. To the best of our knowledge, our work is the first to simulate the complex fracture patterns of single‐layered membranes in computer graphics and introduce heterogeneity induced by the diffusion process, which generates more geometrically rich fracture patterns. Our end‐to‐end 3D simulations show that our deformation‐diffusion coupling framework captures detailed fracture growth patterns in thin membranes due to both in‐plane and out‐of‐plane motions, producing realistically wrinkled slit edges, and heterogeneity introduced due to diffusion. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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13. A unified second-order accurate in time MPM formulation for simulating viscoelastic liquids with phase change.
- Author
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Su, Haozhe, Xue, Tao, Han, Chengguizi, Jiang, Chenfanfu, and Aanjaneya, Mridul
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MATERIAL point method ,TIME integration scheme ,VISCOSITY ,RAPID prototyping ,LIQUIDS - Abstract
We assume that the viscous forces in any liquid are simultaneously local and non-local, and introduce the extended POM-POM model [McLeish and Larson 1998; Oishi et al. 2012; Verbeeten et al. 2001] to computer graphics to design a unified constitutive model for viscosity that generalizes prior models, such as Oldroyd-B, the Upper-convected Maxwell (UCM) model [Sadeghy et al. 2005], and classical Newtonian viscosity under one umbrella, recovering each of them with different parameter values. Implicit discretization of our model via backward Euler recovers the variational Stokes solver of [Larionov et al. 2017] for Newtonian viscosity. For greater accuracy, however, we introduce the second-order accurate Generalized Single Step Single Solve (GS4) scheme [Tamma et al. 2000; Zhou and Tamma 2004] to computer graphics, which recovers all prior second-order accurate time integration schemes to date. Using GS4 and our generalized constitutive model, we present a Material Point Method (MPM) for simulating various viscoelastic liquid behaviors, such as classical liquid rope coiling, buckling, folding, and shear thinning/thickening. In addition, we show how to couple our viscoelastic liquid simulator with the recently introduced non-Fourier heat diffusion solver [Xue et al. 2020] for simulating problems with phase change, such as melting chocolate and digital fabrication with 3D printing. While the discretization of heat diffusion is slightly different within GS4, we show that it can still be efficiently solved using an assembly-free Multigrid-preconditioned Conjugate Gradients solver. We present end-to-end 3D simulations to demonstrate the versatility of our framework. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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14. A novel discretization and numerical solver for non-fourier diffusion.
- Author
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Xue, Tao, Su, Haozhe, Han, Chengguizi, Jiang, Chenfanfu, and Aanjaneya, Mridul
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MATERIAL point method ,BOLTZMANN'S equation ,DIFFUSION ,POROUS materials ,COMPUTER graphics - Abstract
We introduce the C-F diffusion model [Anderson and Tamma 2006; Xue et al. 2018] to computer graphics for diffusion-driven problems that has several attractive properties: (a) it fundamentally explains diffusion from the perspective of the non-equilibrium statistical mechanical Boltzmann Transport Equation, (b) it allows for a finite propagation speed for diffusion, in contrast to the widely employed Fick's/Fourier's law, and (c) it can capture some of the most characteristic visual aspects of diffusion-driven physics, such as hydrogel swelling, limited diffusive domain for smoke flow, snowflake and dendrite formation, that span from Fourier-type to non-Fourier-type diffusive phenomena. We propose a unified convection-diffusion formulation using this model that treats both the diffusive quantity and its associated flux as the primary unknowns, and that recovers the traditional Fourier-type diffusion as a limiting case. We design a novel semi-implicit discretization for this formulation on staggered MAC grids and a geometric Multigrid-preconditioned Conjugate Gradients solver for efficient numerical solution. To highlight the efficacy of our method, we demonstrate end-to-end examples of elastic porous media simulated with the Material Point Method (MPM), and diffusion-driven Eulerian incompressible fluids. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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15. An adaptive variational finite difference framework for efficient symmetric octree viscosity.
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Goldade, Ryan, Wang, Yipeng, Aanjaneya, Mridul, and Batty, Christopher
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PRESSURE ,VISCOSITY ,REYNOLDS number ,DISCRETIZATION methods ,VELOCITY ,SYMMETRY - Abstract
While pressure forces are often the bottleneck in (near-)inviscid fluid simulations, viscosity can impose orders of magnitude greater computational costs at lower Reynolds numbers. We propose an implicit octree finite difference discretization that significantly accelerates the solution of the free surface viscosity equations using adaptive staggered grids, while supporting viscous buckling and rotation effects, variable viscosity, and interaction with scripted moving solids. In experimental comparisons against regular grids, our method reduced the number of active velocity degrees of freedom by as much as a factor of 7.7 and reduced linear system solution times by factors between 3.8 and 9.4. We achieve this by developing a novel adaptive variational finite difference methodology for octrees and applying it to the optimization form of the viscosity problem. This yields a linear system that is symmetric positive definite by construction, unlike naive finite difference/volume methods, and much sparser than a hypothetical finite element alternative. Grid refinement studies show spatial convergence at first order in L
∞ and second order in L1 , while the significantly smaller size of the octree linear systems allows for the solution of viscous forces at higher effective resolutions than with regular grids. We demonstrate the practical benefits of our adaptive scheme by replacing the regular grid viscosity step of a commercial liquid simulator (Houdini) to yield large speed-ups, and by incorporating it into an existing inviscid octree simulator to add support for viscous flows. Animations of viscous liquids pouring, bending, stirring, buckling, and melting illustrate that our octree method offers significant computational gains and excellent visual consistency with its regular grid counterpart. [ABSTRACT FROM AUTHOR]- Published
- 2019
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16. An Efficient Solver for Two‐way Coupling Rigid Bodies with Incompressible Flow.
- Author
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Aanjaneya, Mridul
- Subjects
COMPUTATIONAL fluid dynamics ,COMPUTATIONAL physics ,FLUID dynamics ,COMPUTER simulation of fluid dynamics ,DISCRETIZATION methods - Abstract
Abstract: 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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17. Dexterous manipulation and control with volumetric muscles.
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Lee, Seunghwan, Yu, Ri, Park, Jungnam, Aanjaneya, Mridul, Sifakis, Eftychios, and Lee, Jehee
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MUSCLE physiology ,MUSCULOSKELETAL system ,COMPUTER-generated imagery ,APPROXIMATION theory ,COMPUTER simulation - Abstract
We propose a framework for simulation and control of the human musculoskeletal system, capable of reproducing realistic animations of dexterous activities with high-level coordination. We present the first controllable system in this class that incorporates volumetric muscle actuators, tightly coupled with the motion controller, in enhancement of line-segment approximations that prior art is overwhelmingly restricted to. The theoretical framework put forth by our methodology computes all the necessary Jacobians for control, even with the drastically increased dimensionality of the state descriptors associated with three-dimensional, volumetric muscles. The direct coupling of volumetric actuators in the controller allows us to model muscular deficiencies that manifest in shape and geometry, in ways that cannot be captured with line-segment approximations. Our controller is coupled with a trajectory optimization framework, and its efficacy is demonstrated in complex motion tasks such as juggling, and weightlifting sequences with variable anatomic parameters and interaction constraints. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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18. Triangulating the Real Projective Plane
- Author
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Aanjaneya, Mridul, Teillaud, Monique, Department of Computer Science and Engineering [Kharagpur] (CSE), Indian Institute of Technology Kharagpur (IIT Kharagpur), Geometric computing (GEOMETRICA), INRIA Futurs, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria), and INRIA
- Subjects
projective geometry ,algorithm ,simplicial complex ,triangulation ,Computer Science::Computational Geometry ,[INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG] ,Computational geometry - Abstract
We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane.
- Published
- 2007
19. Faultfree Tromino Tilings of Rectangles
- Author
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Aanjaneya, Mridul and Pal, Sudebkumar Prasant
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FOS: Mathematics ,Mathematics - Combinatorics ,Combinatorics (math.CO) ,Computer Science::Computational Geometry - Abstract
In this paper we consider faultfree tromino tilings of rectangles and characterize rectangles that admit such tilings. We introduce the notion of {\it crossing numbers} for tilings and derive bounds on the crossing numbers of faultfree tilings. We develop an iterative scheme for generating faultfree tromino tilings for rectangles and derive the closed form expression for the exact number of faultfree tromino tilings for $4\times3t$ rectangles and the exact generating function for $5\times 3t$ rectangles, $t\geq 1$. Our iterative scheme generalizes to arbitrary rectangles; for $6\times 6t$ and $7\times 6t$ rectangles, $t\geq 1$, we derive generating functions for estimating lower bounds on the number of faultfree tilings. We also derive an upper bound on the number of tromino tilings of an $m\times n$ rectangle, where $3|mn$ and $m,n>0$., 34 pages, 17 figures
- Published
- 2006
20. Power diagrams and sparse paged grids for high resolution adaptive liquids.
- Author
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Aanjaneya, Mridul, Gao, Ming, Liu, Haixiang, Batty, Christopher, and Sifakis, Eftychios
- Subjects
OCTREES (Computer graphics) ,COMPUTER graphics ,DIGITAL image processing ,POISSON processes ,FLUIDS ,COMPUTER simulation - Abstract
We present an efficient and scalable octree-inspired fluid simulation framework with the flexibility to leverage adaptivity in any part of the computational domain, even when resolution transitions reach the free surface. Our methodology ensures symmetry, definiteness and second order accuracy of the discrete Poisson operator, and eliminates numerical and visual artifacts of prior octree schemes. This is achieved by adapting the operators acting on the octree's simulation variables to reflect the structure and connectivity of a power diagram, which recovers primal-dual mesh orthogonality and eliminates problematic T-junction configurations. We show how such operators can be efficiently implemented using a pyramid of sparsely populated uniform grids, enhancing the regularity of operations and facilitating parallelization. A novel scheme is proposed for encoding the topology of the power diagram in the neighborhood of each octree cell, allowing us to locally reconstruct it on the fly via a lookup table, rather than resorting to costly explicit meshing. The pressure Poisson equation is solved via a highly efficient, matrix-free multigrid preconditioner for Conjugate Gradient, adapted to the power diagram discretization. We use another sparsely populated uniform grid for high resolution interface tracking with a narrow band level set representation. Using the recently introduced SPGrid data structure, sparse uniform grids in both the power diagram discretization and our narrow band level set can be compactly stored and efficiently updated via streaming operations. Additionally, we present enhancements to adaptive level set advection, velocity extrapolation, and the fast marching method for redistancing. Our overall framework gracefully accommodates the task of dynamically adapting the octree topology during simulation. We demonstrate end-to-end simulations of complex adaptive flows in irregularly shaped domains, with tens of millions of degrees of freedom. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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21. A scalable Schur-complement fluids solver for heterogeneous compute platforms.
- Author
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Liu, Haixiang, Mitchell, Nathan, Aanjaneya, Mridul, and Sifakis, Eftychios
- Subjects
POISSON'S equation ,MULTIGRID methods (Numerical analysis) ,HETEROGENEOUS computing ,HYDRAULICS ,GRAPHICS processing units - Abstract
AbstractWe present a scalable parallel solver for the pressure Poisson equation in fluids simulation which can accommodate complex irregular domains in the order of a billion degrees of freedom, using a single server or workstation fitted with GPU or Many-Core accelerators. The design of our numerical technique is attuned to the subtleties of heterogeneous computing, and allows us to benefit from the high memory and compute bandwidth of GPU accelerators even for problems that are too large to fit entirely on GPU memory. This is achieved via algebraic formulations that adequately increase the density of the GPU-hosted computation as to hide the overhead of offloading from the CPU, in exchange for accelerated convergence. Our solver follows the principles of Domain Decomposition techniques, and is based on the Schur complement method for elliptic partial differential equations. A large uniform grid is partitioned in non-overlapping subdomains, and bandwidth-optimized (GPU or Many-Core) accelerator cards are used to efficiently and concurrently solve independent Poisson problems on each resulting subdomain. Our novel contributions are centered on the careful steps necessary to assemble an accurate global solver from these constituent blocks, while avoiding excessive communication or dense linear algebra. We ultimately produce a highly effective Conjugate Gradients preconditioner, and demonstrate scalable and accurate performance on high-resolution simulations of water and smoke flow. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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22. Non-manifold level sets.
- Author
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Mitchell, Nathan, Aanjaneya, Mridul, Setaluri, Rajsekhar, and Sifakis, Eftychios
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LEVEL set methods ,MANIFOLDS (Mathematics) ,SKILLS inventories ,GRAPHIC arts ,SIMPLE machines ,CRYSTALLIZED intelligence - Abstract
Level sets have been established as highly versatile implicit surface representations, with widespread use in graphics applications including modeling and dynamic simulation. Nevertheless, level sets are often presumed to be limited, compared to explicit meshes, in their ability to represent domains with thin topological features (e.g. narrow slits and gaps) or, even worse, material overlap. Geometries with such features may arise from modeling tools that tolerate occasional self-intersections, fracture modeling algorithms that create narrow or zero-width cuts by design, or as transient states in collision processing pipelines for deformable objects. Converting such models to level sets can alter their topology if thin features are not resolved by the grid size. We argue that this ostensible limitation is not an inherent defect of the implicit surface concept, but a collateral consequence of the standard Cartesian lattice used to store the level set values. We propose storing signed distance values on a regular hexahedral mesh which can have multiple collocated cubic elements and non-manifold bifurcation to accommodate non-trivial topology. We show how such non-manifold level sets can be systematically generated from convenient alternative geometric representations. Finally we demonstrate how this representation can facilitate fast and robust treatment of self-collision in simulations of volumetric elastic deformable bodies. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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23. 3D City Modeling from Street-Level Data for Augmented Reality Applications.
- Author
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Pylvanainen, Timo, Berclaz, Jerome, Korah, Thommen, Hedau, Varsha, Aanjaneya, Mridul, and Grzeszczuk, Radek
- Abstract
We present a method for automatically creating compact and accurate 3D city models needed for enhanced Augmented Reality applications. The input data are panorama images and LIDAR scans collected at street level and positioned using an IMU and a GPS. Our method corrects for the GPS error and the IMU drift to produce a globally consistent and well registered dataset for the whole city. We use structure from motion and skyline detection to complement the limited range of LIDAR data. Additionally, we propose a novel reconstruction technique that exploits architectural properties of urban environments to create an accurate 3D city model from incomplete data. Our method is able to process an entire city, or several terabytes of data, in a matter of days. We show that our reconstruction achieves higher accuracy than a commercial solution. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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24. Mass and momentum conservation for fluid simulation.
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Lentine, Michael, Aanjaneya, Mridul, and Fedkiw, Ronald
- Published
- 2011
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25. Metric graph reconstruction from noisy data.
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Aanjaneya, Mridul, Chazal, Frederic, Chen, Daniel, Glisse, Marc, Guibas, Leonidas J., and Morozov, Dmitriy
- Published
- 2011
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26. METRIC GRAPH RECONSTRUCTION FROM NOISY DATA.
- Author
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AANJANEYA, MRIDUL, CHAZAL, FREDERIC, CHEN, DANIEL, GLISSE, MARC, GUIBAS, LEONIDAS, and MOROZOV, DMITRIY
- Subjects
- *
SIGNAL-to-noise ratio , *METRIC spaces , *ALGORITHMS , *HOMEOMORPHISMS , *INFERENTIAL statistics , *CORRESPONDENCE analysis (Statistics) , *MATHEMATICAL inequalities - Abstract
Many real-world data sets can be viewed of as noisy samples of special types of metric spaces called metric graphs. Building on the notions of correspondence and Gromov-Hausdorff distance in metric geometry, we describe a model for such data sets as an approximation of an underlying metric graph. We present a novel algorithm that takes as an input such a data set, and outputs a metric graph that is homeomorphic to the underlying metric graph and has bounded distortion of distances. We also implement the algorithm, and evaluate its performance on a variety of real world data sets. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
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27. Constraint bubbles and affine regions: reduced fluid models for efficient immersed bubbles and flexible spatial coarsening.
- Author
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Goldade, Ryan, Aanjaneya, Mridul, and Batty, Christopher
- Subjects
BUBBLES ,OPEN-channel flow ,DEGREES of freedom ,VECTOR fields ,GRID cells ,ORTHOGRAPHIC projection - Abstract
We propose to enhance the capability of standard free-surface flow simulators with efficient support for immersed bubbles through two new models: constraint-based bubbles and affine fluid regions. Unlike its predecessors, our constraint-based model entirely dispenses with the need for advection or projection inside zero-density bubbles, with extremely modest additional computational overhead that is proportional to the surface area of all bubbles. This surface-only approach is easy to implement, realistically captures many familiar bubble behaviors, and even allows two or more distinct liquid bodies to correctly interact across completely unsimulated air. We augment this model with a per-bubble volume-tracking and correction framework to minimize the cumulative effects of gradual volume drift. To support bubbles with non-zero densities, we propose a novel reduced model for an irregular fluid region with a single pointwise incompressible affine vector field. This model requires only 11 interior velocity degrees of freedom per affine fluid region in 3D, and correctly reproduces buoyant, stationary, and sinking behaviors of a secondary fluid phase with non-zero density immersed in water. Since the pressure projection step in both the above schemes is a slightly modified Poisson-style system, we propose novel Multigrid-based preconditioners for Conjugate Gradients for fast numerical solutions of our new discretizations. Furthermore, we observe that by enforcing an incompressible affine vector field over a coalesced set of grid cells, our reduced model is effectively an irregular coarse super-cell. This offers a convenient and flexible adaptive coarsening strategy that integrates readily with the standard staggered grid approach for fluid simulation, yet supports coarsened regions that are arbitrary voxelized shapes, and provides an analytically divergence-free interior. We demonstrate its effectiveness with a new adaptive liquid simulator whose interior regions are coarsened into a mix of tiles with regular and irregular shapes. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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28. IQ-MPM: an interface quadrature material point method for non-sticky strongly two-way coupled nonlinear solids and fluids.
- Author
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Fang, Yu, Qu, Ziyin, Li, Minchen, Zhang, Xinxin, Zhu, Yixin, Aanjaneya, Mridul, and Jiang, Chenfanfu
- Subjects
MATERIAL point method ,ELASTIC solids ,FLUIDS - Abstract
We propose a novel scheme for simulating two-way coupled interactions between nonlinear elastic solids and incompressible fluids. The key ingredient of this approach is a ghost matrix operator-splitting scheme for strongly coupled nonlinear elastica and incompressible fluids through the weak form of their governing equations. This leads to a stable and efficient method handling large time steps under the CFL limit while using a single monolithic solve for the coupled pressure fields, even in the case with highly nonlinear elastic solids. The use of the Material Point Method (MPM) is essential in the designing of the scheme, it not only preserves discretization consistency with the hybrid Lagrangian-Eulerian fluid solver, but also works naturally with our novel interface quadrature (IQ) discretization for free-slip boundary conditions. While traditional MPM suffers from sticky numerical artifacts, our framework naturally supports discontinuous tangential velocities at the solid-fluid interface. Our IQ discretization results in an easy-to-implement, fully particle-based treatment of the interfacial boundary, avoiding the additional complexities associated with intermediate level set or explicit mesh representations. The efficacy of the proposed scheme is verified by various challenging simulations with fluid-elastica interactions. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
29. Giga Graph Cities: Their Buckets, Buildings, Waves, and Fragments.
- Author
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Abello J, Zhang H, Nakhimovich D, Han C, and Aanjaneya M
- Abstract
Graph Cities are the 3-D visual representations of partitions of a graph edge set into maximal connected subgraphs, each of which is called a fixed point of degree peeling. Each such connected subgraph is visually represented as a Building. A polylog bucketization of the size distribution of the subgraphs represented by the buildings generates a 2-D position for each bucket. The Delaunay triangulation of the bucket building locations determines the street network. We illustrate Graph Cities for the Friendster social network (1.8 billion edges), a co-occurrence keywords network derived from the Internet Movie Database (115 million edges), and a patent citation network (16.5 million edges). Up to 2 billion edges, all the elements of their corresponding Graph Cities are built in a few minutes (excluding I/O time). Our ultimate goal is to provide tools to build humanly interpretable descriptions of any graph, without being constrained by the graph size.
- Published
- 2022
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