Results 1 - 10 of 1,695

Modifying CLJP to Select Grid Hierarchies with Lower Operator Complexities and Better Performance ∗

by David M. Alber
"... Algebraic multigrid (AMG) is an efficient algorithm for solving certain types of large, sparse linear systems. For solving very large problems with AMG it becomes necessary to use parallel algorithms. Coarse grid selection algorithms such as CLJP were created to parallelize the setup phase of AMG. F ..."
Abstract - Cited by 2 (2 self) - Add to MetaCart
Algebraic multigrid (AMG) is an efficient algorithm for solving certain types of large, sparse linear systems. For solving very large problems with AMG it becomes necessary to use parallel algorithms. Coarse grid selection algorithms such as CLJP were created to parallelize the setup phase of AMG

Monte Carlo Localization: Efficient Position Estimation for Mobile Robots

by Dieter Fox, Wolfram Burgard, Frank Dellaert, Sebastian Thrun - IN PROC. OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI , 1999
"... This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computational ..."
Abstract - Cited by 343 (46 self) - Add to MetaCart
computationally cumbersome (such as grid-based approaches that represent the state space by high-resolution 3D grids), or had to resort to extremely coarse-grained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies sampling

Real-Time, Continuous Level of Detail Rendering of Height Fields

by Peter Lindstrom , David Koller, William Ribarsky, Larry F. Hodges, Nick Faust, Gregory A. Turner , 1996
"... We present an algorithm for real-time level of detail reduction and display of high-complexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screen-space threshold to bound the maximum error of the projected image. A coarse lev ..."
Abstract - Cited by 296 (15 self) - Add to MetaCart
We present an algorithm for real-time level of detail reduction and display of high-complexity polygonal surface data. The algorithm uses a compact and efficient regular grid representation, and employs a variable screen-space threshold to bound the maximum error of the projected image. A coarse

Genetic Algorithms, Noise, and the Sizing of Populations

by David E. Goldberg, Kalyanmoy Deb, James H. Clark - 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 - Cited by 276 (85 self) - Add to MetaCart
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

Efficient Setup . . .

by David Michael Alber , 2007
"... Solving partial differential equations (PDEs) using analytical techniques is intractable for all but the simplest problems. Many computational approaches to approximate solutions to PDEs yield large systems of linear equations. Algorithms known as linear solvers then compute an approximate solution ..."
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constructs a lower dimensional problem to remove error remaining after relaxation. In algebraic multigrid (AMG), the lower dimensional space is constructed by coarse-grid selection algorithms. In this thesis, an introduction and study of independent set-based parallel coarse-grid selection algorithms

Coarse-grid Selection for Parallel Algebraic Multigrid

by Andrew J. Cleary, Robert D. Falgout, Van Emden Henson, Jim E. Jones - Held at Lawrence Berkeley National Laboratory , 1998
"... . The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarse-grid poin ..."
Abstract - Cited by 25 (3 self) - Add to MetaCart
. The need to solve linear systems arising from problems posed on extremely large, unstructured grids has sparked great interest in parallelizing algebraic multigrid (AMG). To date, however, no parallel AMG algorithms exist. We introduce a parallel algorithm for the selection of coarse-grid

Computing Geodesic Paths on Manifolds

by R. Kimmel, J. A. Sethian - Proc. Natl. Acad. Sci. USA , 1998
"... The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. A ..."
Abstract - Cited by 294 (28 self) - Add to MetaCart
The Fast Marching Method [8] is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity

A greedy strategy for coarse-grid selection

by S. Maclachlan, Yousef Saad , 2006
"... Efficient solution of the very large linear systems that arise in numerical modelling of real-world applications is often only possible through the use of multilevel techniques. While highly optimized algorithms may be developed using knowledge about the origins of the matrix problem to be considere ..."
Abstract - Cited by 10 (4 self) - Add to MetaCart
to be considered, much recent interest has been in the development of purely algebraic approaches that may be applied in many situations, without problem-specific tuning. Here, we consider an algebraic approach to finding the fine/coarse partitions needed in multilevel approaches. The algorithm is motivated

COARSENING INVARIANCE AND BUCKET-SORTED INDEPENDENT SETS FOR ALGEBRAIC MULTIGRID ∗

by David M. Alber, Luke, N. Olson
"... Abstract. Independent set-based coarse-grid selection algorithms for algebraic multigrid are defined by their policies for weight initialization, independent set selection, and weight update. In this paper, we develop theory demonstrating that algorithms employing the same policies produce identical ..."
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Abstract. Independent set-based coarse-grid selection algorithms for algebraic multigrid are defined by their policies for weight initialization, independent set selection, and weight update. In this paper, we develop theory demonstrating that algorithms employing the same policies produce

A cartesian grid method with transient anisotropic adaption

by F. E. Ham, F. S. Lien, A. B. Strong - Journal of Computational Physics
"... A Cartesian grid method with solution-adaptive anisotropic refinement and coars-ening is developed for simulating time-dependent incompressible flows. The Carte-sian grid cells and faces are managed using an unstructured data approach, and al-gorithms are described for the time-accurate transient an ..."
Abstract - Cited by 17 (2 self) - Add to MetaCart
the velocity field using a novel ap-proximate factorization technique, although an iterative technique is also presented. The pressure Poisson equation is solved using additive correction multigrid, and an efficient coarse grid selection algorithm is presented. Finally, the Cartesian cell geometry allows
Results 1 - 10 of 1,695