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Results 1 - 10
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1,607
Visual Simulation of Smoke
, 2001
"... In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer gra ..."
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Cited by 346 (22 self)
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In this paper, we propose a new approach to numerical smoke simulation for computer graphics applications. The method proposed here exploits physics unique to smoke in order to design a numerical method that is both fast and efficient on the relatively coarse grids traditionally used in computer
Deciding the nature of the coarse equation through microscopic simulations: the Baby-Bathwater scheme
- SIAM MMS
"... Abstract. Recent developments in multiscale computation allow the solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations in closed form. The closure is obtained on demand through appropriately initialized ..."
Abstract
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Cited by 23 (10 self)
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initialized bursts of microscopic simulation. The effective coupling of microscopic simulators with macrosocopic behavior requires certain decisions about the nature of the unavailable coarse equation. Such decisions include (a) the highest spatial derivative active in the coarse equation, (b) whether
Genetic Algorithms, Noise, and the Sizing of Populations
- COMPLEX SYSTEMS
, 1991
"... This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of building-block fitness or so-called collateral noise is the major source of variance, and a population-sizing equation is derived to ensure that average sig ..."
Abstract
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Cited by 276 (85 self)
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equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior. At low population sizes the GA makes many errors of decision, and the quality of convergence is largely left to the vagaries of chance or the serial fixup of flawed
Dynamic Real-Time Deformations using Space Time Adaptive Sampling
, 2001
"... This paper presents a robust, adaptive method for animating dynamic visco-elastic deformable objects that provides a guaranteed frame rate. Our approach uses a novel automatic space and time adaptive level of detail technique, in combination with a largedisplacement (Green) strain tensor formulation ..."
Abstract
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Cited by 226 (14 self)
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formulation. The body is partitioned in a non-nested multiresolution hierarchy of tetrahedral meshes. The local resolution is determined by a quality condition that indicates where and when the resolution is too coarse. As the object moves and deforms, the sampling is refined to concentrate the computational
Gene regulatory networks: A coarse-grained, equation-free approach to multiscale computation
- J. Chem. Phys
, 2006
"... Abstract: We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution of appropriately-initialized short bursts of stochastic simulations; the results of these are processed to ..."
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Cited by 24 (10 self)
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to estimate coarse-grained quantities of interest, such as mesoscopic transport coefficients. In particular, using a simple model of a genetic toggle switch, we illustrate the computation of an effective free energy Φ and of a state-dependent effective diffusion coefficient D that characterize an unavailable
Asymptotics, frequency modulation, and low regularity ill-posedness for canonical defocusing equations
- AMER. J. MATH
, 2002
"... In a recent paper [18], Kenig, Ponce and Vega study the low regularity behavior of the focusing nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex Korteweg-de Vries (KdV) equations. Using soliton and breather solutions, they demonstrate the lack of local well-posed ..."
Abstract
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Cited by 128 (13 self)
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-posedness for these equations below their respective endpoint regularities. In this paper, we study the defocusing analogues of these equations, namely defocusing NLS, defocusing mKdV, and real KdV, all in one spatial dimension, for which suitable soliton and breather solutions are unavailable. We construct for each
A Conservative Adaptive Projection Method for the Variable Density Incompressible Navier–Stokes Equations
- JOURNAL OF COMPUTATIONAL PHYSICS 142, 1–46 (1998)
, 1998
"... In this paper we present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advection–diffusion equations to predict in ..."
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Cited by 131 (28 self)
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In this paper we present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advection–diffusion equations to predict
Schwarz Analysis Of Iterative Substructuring Algorithms For Elliptic Problems In Three Dimensions
- SIAM J. Numer. Anal
, 1993
"... . Domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations of partial differential equations. The preconditioners are constructed from exact or approximate sol ..."
Abstract
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Cited by 147 (33 self)
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solvers for the same partial differential equation restricted to a set of subregions into which the given region has been divided. In addition, the preconditioner is often augmented by a coarse, second level approximation, that provides additional, global exchange of information, and which can enhance
Kevrekidis, Equation-free modelling of evolving diseases: coarse-grained computations with individual-based models, Proc Roy Soc
"... We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. Sidestepping the necessity of obtaining explicit population-level models, the approach analyzes the (unavailable in clo ..."
Abstract
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Cited by 7 (0 self)
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in closed form) ‘coarse ’ macroscopic equations, estimating the necessary quantities through appropriately initialized, short ‘bursts ’ of individual-based dynamic simulation. We illustrate this approach by analyzing a stochastic and discrete model for the evolution of disease agents caused by point
Accuracy and Stability of the Coarse Time-Stepper for a Lattice Boltzmann Model
, 2007
"... The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the unavailable macroscopic model when only a microscopic simulator is given. In this paper, we study the numerical properties of the coarse tim ..."
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Cited by 3 (3 self)
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The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the unavailable macroscopic model when only a microscopic simulator is given. In this paper, we study the numerical properties of the coarse
Results 1 - 10
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