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35
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 ..."
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Cited by 31 (2 self)
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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.
Fluid Interaction for High Resolution WallSize Displays
, 2002
"... that I have read this dissertation and that in my opinion it is fully adequate, ..."
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Cited by 20 (2 self)
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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 ..."
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Cited by 18 (12 self)
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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...
On the qpolynomials: a distributional study
, 2001
"... In this paper we present a uni ed distributional study of the classical discrete qpolynomials (in the Hahn’s sense). From the distributional qPearson equation we will deduce many of their properties such as the threeterm recurrence relations, structure relations, etc. Also several characterizatio ..."
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Cited by 17 (5 self)
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In this paper we present a uni ed distributional study of the classical discrete qpolynomials (in the Hahn’s sense). From the distributional qPearson equation we will deduce many of their properties such as the threeterm recurrence relations, structure relations, etc. Also several characterizations of such qpolynomials are presented.
The Science of Deriving Dense Linear Algebra Algorithms
, 2002
"... In this paper we present a systematic approach to the derivation of families of highperformance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is given. The paper is structured ..."
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Cited by 16 (8 self)
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In this paper we present a systematic approach to the derivation of families of highperformance algorithms for a large set of frequently encountered dense linear algebra operations. As part of the derivation a constructive proof of the correctness of the algorithm is given. The paper is structured so that it can be used as a tutorial for novices. However, the method has been shown to yield new, highperformance algorithms for wellstudied linear algebra operations and should also be of interest to the "high priests of high performance."
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 ..."
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Cited by 14 (10 self)
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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 ..."
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Cited by 13 (7 self)
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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.
Electroweak Penguin Contributions to NonLeptonic ∆F = 1 Decays at NNLO
, 1999
"... We calculate the O(αs) corrections to the Z0penguin and electroweak box diagrams relevant for nonleptonic ∆F = 1 decays with F = S, B. This calculation provides the complete O(αWαs) and O(αWαs sin 2 θWm2 t) corrections (αW = α / sin 2 θW) to the Wilson coefficients of the electroweak penguin four ..."
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Cited by 5 (3 self)
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We calculate the O(αs) corrections to the Z0penguin and electroweak box diagrams relevant for nonleptonic ∆F = 1 decays with F = S, B. This calculation provides the complete O(αWαs) and O(αWαs sin 2 θWm2 t) corrections (αW = α / sin 2 θW) to the Wilson coefficients of the electroweak penguin four quark operators relevant for nonleptonic K and Bdecays. We argue that this is the dominant part of the nextnexttoleading (NNLO) contributions to these coefficients. Our results allow to reduce considerably the uncertainty due to the definition of the top quark mass present in the existing NLO calculations of nonleptonic decays. The NNLO corrections to the coefficient of the color singlet (V − A) ⊗ (V − A) electroweak penguin operator Q9 relevant for Bdecays are generally moderate, amount to a few percent for the choice mt(µt = mt) and depend only weakly on the renormalization scheme. Larger NNLO corrections with substantial scheme dependence are found for the coefficients of the remaining electroweak penguin operators Q7, Q8 and Q10. In particular, the strong scheme dependence of the NNLO corrections to
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 ..."
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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 ..."
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Cited by 3 (1 self)
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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