Results 1 - 10 of 5,801

Unified analysis of discontinuous Galerkin methods for elliptic problems

by Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, L. Donatella Marini - SIAM J. Numer. Anal , 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
Abstract - Cited by 525 (31 self) - Add to MetaCart
Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical

AN EFFICIENT PARALLEL DISCRETE PDE SOLVER

by unknown authors , 1994
"... Abstract We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special rece ..."
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Abstract We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special

Approximating discrete probability distributions with dependence trees

by C. K. Chow, C. N. Liu - IEEE TRANSACTIONS ON INFORMATION THEORY , 1968
"... A method is presented to approximate optimally an n-dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n-1 first order dependence relationship among the n variables ..."
Abstract - Cited by 881 (0 self) - Add to MetaCart
A method is presented to approximate optimally an n-dimensional discrete probability distribution by a product of second-order distributions, or the distribution of the first-order tree dependence. The problem is to find an optimum set of n-1 first order dependence relationship among the n

Symmetry and Related Properties via the Maximum Principle

by B. Gidas, Wei-ming Ni, L. Nirenberg , 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
Abstract - Cited by 538 (4 self) - Add to MetaCart
We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting

Discrete Differential-Geometry Operators for Triangulated 2-Manifolds

by Mark Meyer, Mathieu Desbrun, Peter Schröder, Alan H. Barr , 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 ..."
Abstract - Cited by 449 (14 self) - Add to MetaCart
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

Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order

by Etienne Pardoux - in Stochastic Analysis and Related Topics VI: The Geilo Workshop , 1996
"... The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs have ..."
Abstract - Cited by 260 (15 self) - Add to MetaCart
The aim of this set of lectures is to present the theory of backward stochastic differential equations, in short BSDEs, and its connections with viscosity solutions of systems of semi– linear second order partial differential equations of parabolic and elliptic type, in short PDEs. Linear BSDEs

HOMOGENIZATION AND TWO-SCALE CONVERGENCE

by Gregoire Allaire , 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "two-scale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector- ..."
Abstract - Cited by 451 (14 self) - Add to MetaCart
linear and nonlinear second-order elliptic equations.

An Efficient Parallel Discrete PD Solver

by Y. Notay, Service De M'etrologie Nucl'eaire - Parallel Computing , 1994
"... We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently deve ..."
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We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently

A multilevel block incomplete factorization preconditioning

by Y. Notay - APPLIED NUMERICAL MATHEMATICS 31 (1999) 209–225 , 1999
"... Incomplete factorization preconditioners based on recursive red–black orderings have been shown efficient for discrete second order elliptic PDEs with isotropic coefficients. However, they suffer for some weakness in presence of anisotropy or grid stretching. Here we propose to combine these orderin ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
Incomplete factorization preconditioners based on recursive red–black orderings have been shown efficient for discrete second order elliptic PDEs with isotropic coefficients. However, they suffer for some weakness in presence of anisotropy or grid stretching. Here we propose to combine

Optimal V cycle algebraic multilevel preconditioning

by Y. Notay , 1997
"... We consider algebraic multilevel preconditioning methods based on the recursive use of a 2 x 2 block incomplete factorization procedure in which the Schur complement is approximated by a coarse grid matrix. As is well known, for discrete second order elliptic PDEs, optimal convergence properties are ..."
Abstract - Cited by 5 (4 self) - Add to MetaCart
We consider algebraic multilevel preconditioning methods based on the recursive use of a 2 x 2 block incomplete factorization procedure in which the Schur complement is approximated by a coarse grid matrix. As is well known, for discrete second order elliptic PDEs, optimal convergence properties
Results 1 - 10 of 5,801