Results 1  10
of
23
Fluid Interaction for High Resolution WallSize Displays
, 2002
"... that I have read this dissertation and that in my opinion it is fully adequate, ..."
Abstract

Cited by 17 (2 self)
 Add to MetaCart
that I have read this dissertation and that in my opinion it is fully adequate,
Algorithmic Integrability Tests for Nonlinear Differential and Lattice Equations
 Computer Physics Communications
, 1999
"... Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differentialdifference equations are presented. The first algorithm is the wellknown Painlev e test, which is applicable to polynomial systems of ordinary and partial differential equations. T ..."
Abstract

Cited by 17 (12 self)
 Add to MetaCart
Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differentialdifference equations are presented. The first algorithm is the wellknown Painlev e test, which is applicable to polynomial systems of ordinary and partial differential equations. The second and third algorithms allow one to explicitly compute polynomial conserved densities and higherorder symmetries of nonlinear evolution and lattice equations. The first algorithm is implemented in the symbolic syntax of both Macsyma and Mathematica. The second and third algorithms are available in Mathematica. The codes can be used for computeraided integrability testing of nonlinear di erential and lattice equations as they occur in various branches of the sciences and engineering. Applied to systems with parameters, the codes can determine the conditions on the parameters so that the systems pass the Painlevé test, or admit a sequence of conserved densities or higherorder symmetries...
Lowstorage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations
, 2000
"... The derivation of lowstorage, explicit Runge–Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier–Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy effici ..."
Abstract

Cited by 15 (2 self)
 Add to MetaCart
The derivation of lowstorage, explicit Runge–Kutta (ERK) schemes has been performed in the context of integrating the compressible Navier–Stokes equations via direct numerical simulation. Optimization of ERK methods is done across the broad range of properties, such as stability and accuracy efficiency, linear and nonlinear stability, error control reliability, step change stability, and dissipation/dispersion accuracy, subject to varying degrees of memory economization. Following van der Houwen and Wray, sixteen ERK pairs are presented using from two to five registers of memory per equation, per grid point and having accuracies from third to fifthorder. Methods have been tested with not only DETEST, but also with the 1D wave equation. Two of the methods have been applied to the DNS of a compressible jet as well as methaneair and hydrogenair flames. Derived 3(2) and 4(3) pairs are competitive with existing fullstorage methods. Although a substantial efficiency penalty accompanies use of two and threeregister, fifthorder methods, the best contemporary fullstorage methods can be nearly matched while still saving 2–3 registers of memory.
Computation of Conservation Laws for Nonlinear Lattices
 Physica D
, 1998
"... An algorithm to compute polynomial conserved densities of polynomial nonlinear lattices is presented. The algorithm is implemented in Mathematica and can be used as an automated integrability test. With the code didens.m, conserved densities are obtained for several wellknown lattice equations. For ..."
Abstract

Cited by 12 (9 self)
 Add to MetaCart
An algorithm to compute polynomial conserved densities of polynomial nonlinear lattices is presented. The algorithm is implemented in Mathematica and can be used as an automated integrability test. With the code didens.m, conserved densities are obtained for several wellknown lattice equations. For systems with parameters, the code allows one to determine the conditions on these parameters so that a sequence of conservation laws exist. Keywords: Conservation law; Integrability; Semidiscrete; Lattice 1 Introduction There are several motives to nd the explicit form of conserved densities of dierentialdierence equations (DDEs). The rst few conservation laws have a physical meaning, such as conservation of momentum and energy. Additional ones facilitate the study of both quantitative and qualitative properties of solutions [1]. Furthermore, the existence of a sequence of conserved densities predicts integrability. Yet, the nonexistence of polynomial conserved quantities does not p...
Algorithmic computation of higherorder symmetries for nonlinear evolution and lattice equations Adv
 Comput. Math
, 1999
"... A straightforward algorithm for the symbolic computation of higherorder symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the polynomial form of the higherorder symmetries. The coeffici ..."
Abstract

Cited by 11 (6 self)
 Add to MetaCart
A straightforward algorithm for the symbolic computation of higherorder symmetries of nonlinear evolution equations and lattice equations is presented. The scaling properties of the evolution or lattice equations are used to determine the polynomial form of the higherorder symmetries. The coefficients of the symmetry can be found by solving a linear system. The method applies to polynomial systems of PDEs of firstorder in time and arbitrary order in one space variable. Likewise, lattices must be of first order in time but may involve arbitrary shifts in the discretized space variable. The algorithm is implemented in Mathematica and can be used to test the integrability of both nonlinear evolution equations and semidiscrete lattice equations. With our Integrability Package, higherorder symmetries are obtained for several wellknown systems of evolution and lattice equations. For PDEs and lattices with parameters, the code allows one to determine the conditions on these parameters so that a sequence of higherorder symmetries exist. The existence of a sequence of such symmetries is a predictor for integrability.
Families of Algorithms Related to the Inversion of a Symmetric Positive Definite Matrix
"... We study the highperformance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three “sweeps”: a Cho ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We study the highperformance implementation of the inversion of a Symmetric Positive Definite (SPD) matrix on architectures ranging from sequential processors to Symmetric MultiProcessors to distributed memory parallel computers. This inversion is traditionally accomplished in three “sweeps”: a Cholesky factorization of the SPD matrix, the inversion of the resulting triangular matrix, and finally the multiplication of the inverted triangular matrix by its own transpose. We state different algorithms for each of these sweeps as well as algorithms that compute the result in a single sweep. One algorithm outperforms the current ScaLAPACK implementation by 2030 percent due to improved loadbalance on a distributed memory architecture.
The Science of Programming HighPerformance Linear Algebra Libraries
, 2002
"... When considering the unmanageable complexity of computer systems, Dijkstra recently made the following observations: 1. When exhaustive testing is impossible  i.e., almost always  our trust can only be based on proof (be it mechanized or not). 2. A program ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
When considering the unmanageable complexity of computer systems, Dijkstra recently made the following observations: 1. When exhaustive testing is impossible  i.e., almost always  our trust can only be based on proof (be it mechanized or not). 2. A program
Minimum Description Length And The Inference Of Scene Structure From Images
 In IEE Colloquium on Applied Statistical Pattern Recognition
, 1999
"... Introduction Model selection is a central task in computer vision: given data obtained from images and given a number of models, which model is most strongly supported by the data? Is it better to have i) a simple model fitting the data approximately; or ii) a complicated model fitting the data ver ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Introduction Model selection is a central task in computer vision: given data obtained from images and given a number of models, which model is most strongly supported by the data? Is it better to have i) a simple model fitting the data approximately; or ii) a complicated model fitting the data very closely [3],[4], [9],[11]? In many cases the models vary widely in complexity and flexibility, and there is little prior knowledge about the best choice of model. The Minimum Description Length (MDL) method links model selection to data compression: the best model is the one which yields the largest compression of the data. The general theoretical framework for compression is Kolmogorov complexity: let x, y be bit strings, ie. elements of \Sigma = f0; 1g . The Kolmogorov complexity K(xjy) of x conditional o
Simplified Grid Computing through Spreadsheets and NetSolve
"... Grid computing has great potential but to enter the mainstream it must be simplified. Tools and libraries must make it easier to solve problems by being simpler and at the same time more sophisticated. In this paper we describe how Grid computing can be achieved through spreadsheets. No parallel pro ..."
Abstract
 Add to MetaCart
Grid computing has great potential but to enter the mainstream it must be simplified. Tools and libraries must make it easier to solve problems by being simpler and at the same time more sophisticated. In this paper we describe how Grid computing can be achieved through spreadsheets. No parallel programming or complex tools need to be used. So long as dependencies allow it, formulae in a spreadsheet can be evaluated concurrently on the Grid. Thus Grid computing becomes accessible to all those who can use a spreadsheet. The story is completed with a sophisticated backend system, NetSolve, which can solve complex linear algebra systems with minimal intervention from the user. In this paper we present the architecture of the system for performing such simple yet sophisticated grid computing and a case study which performs a large singular value decomposition. 1.