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10,786
A secondorderaccurate symmetric discretization of the Poisson equation on irregular domain
 J. Comput. Phys
"... In this paper, we consider the variable coefficient Poisson equation with Dirichlet boundary conditions on an irregular domain and show that one can obtain second order accuracy with a rather simple discretization. Moreover, since our discretization matrix is symmetric, it can be inverted rather qui ..."
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Cited by 75 (17 self)
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quickly as opposed to the more complicated nonsymmetric discretization matrices found in other second order accurate discretizations of this problem. Multidimensional computational results are presented to demonstrate the second order accuracy of this numerical method. In addition, we use our approach
Approximating discrete probability distributions with dependence trees
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1968
"... A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n variables ..."
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Cited by 881 (0 self)
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A method is presented to approximate optimally an ndimensional discrete probability distribution by a product of secondorder distributions, or the distribution of the firstorder tree dependence. The problem is to find an optimum set of n1 first order dependence relationship among the n
Discrete DifferentialGeometry Operators for Triangulated 2Manifolds
, 2002
"... This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging Vorono ..."
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Cited by 449 (14 self)
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This paper provides a unified and consistent set of flexible tools to approximate important geometric attributes, including normal vectors and curvatures on arbitrary triangle meshes. We present a consistent derivation of these first and second order differential properties using averaging
Efficient belief propagation for early vision
 In CVPR
, 2004
"... Markov random field models provide a robust and unified framework for early vision problems such as stereo, optical flow and image restoration. Inference algorithms based on graph cuts and belief propagation yield accurate results, but despite recent advances are often still too slow for practical u ..."
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Cited by 515 (8 self)
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the standard algorithm by several orders of magnitude. In practice we obtain stereo, optical flow and image restoration algorithms that are as accurate as other global methods (e.g., using the Middlebury stereo benchmark) while being as fast as local techniques. 1
Aerodynamic Design Optimization On Unstructured Meshes Using the NavierStokes Equations
 AIAA J
, 1999
"... A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a secondorder accurate discretization method is described. The relationship between the continuous formulation and a discret ..."
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Cited by 150 (4 self)
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A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a secondorder accurate discretization method is described. The relationship between the continuous formulation and a
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
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Cited by 1397 (38 self)
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, suppose that A is a Gaussian random matrix; then stable recovery occurs for almost all such A's provided that the number of nonzeros of x 0 is of about the same order as the number of observations. As a second instance, suppose one observes few Fourier samples of x 0 ; then stable recovery occurs
A Symmetric Method for Implicit Time Discretization of the Stefan Problem
, 2000
"... In this paper, we propose a symmetric second order accurate discretization of the Poisson equation with Dirichlet boundary conditions on an irregular domain. The symmetric discretization matrix can be inverted rather quickly as opposed to the nonsymmetric discretization matrices found in other secon ..."
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Cited by 3 (2 self)
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In this paper, we propose a symmetric second order accurate discretization of the Poisson equation with Dirichlet boundary conditions on an irregular domain. The symmetric discretization matrix can be inverted rather quickly as opposed to the nonsymmetric discretization matrices found in other
Using the Particle Level Set Method and a Second Order Accurate Pressure Boundary Condition for Free Surface Flows
, 2003
"... In this paper, we present an enhanced resolution capturing method for topologically complex two and three dimensional incompressible free surface flows. The method is based upon the level set method of Osher and Sethian to represent the interface combined with two recent advances in the treatmen ..."
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in the treatment of the interface, a second order accurate discretization of the Dirichlet pressure boundary condition at the free surface (2002, J. Comput. Phys. 176, 205) and the use of massless marker particles to enhance the resolution of the interface through the use of the particle level set method (2002
A highly accurate approach that resolves the pressure spike of elastohydrodynamic lubrication
 J. Tribol
, 1988
"... We propose an accurate numerical method to solve the classical line contact problem of elastohydrodynamic lubrication. The method incorporates a second order accurate discretization and a straightforward automatic local mesh refinement procedure. Using these elements, we remove discretization error ..."
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Cited by 2 (0 self)
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We propose an accurate numerical method to solve the classical line contact problem of elastohydrodynamic lubrication. The method incorporates a second order accurate discretization and a straightforward automatic local mesh refinement procedure. Using these elements, we remove discretization
Cartesian Grid Embedded Boundary Methods for Elliptic and
 Univ. of California, Berkeley
, 1997
"... We present an algorithm for solving the heat equation on irregular timedependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (1998, J. Comput. Phys. 147, 60) for discretizing Poisson’s equation, combined with a secondorder accurate discretization ..."
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Cited by 178 (20 self)
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We present an algorithm for solving the heat equation on irregular timedependent domains. It is based on the Cartesian grid embedded boundary algorithm of Johansen and Colella (1998, J. Comput. Phys. 147, 60) for discretizing Poisson’s equation, combined with a secondorder accurate discretization
Results 1  10
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