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274
Finite differencing of computable expressions
, 1980
"... Finite differencing is a program optimization method that generalizes strength reduction, and provides an efficient implementation for a host of program transformations including "iterator inversion." Finite differencing is formally specified in terms of more basic transformations shown to ..."
Abstract

Cited by 133 (6 self)
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Finite differencing is a program optimization method that generalizes strength reduction, and provides an efficient implementation for a host of program transformations including "iterator inversion." Finite differencing is formally specified in terms of more basic transformations shown
CoArray Fortran Experiences with Finite Differencing Methods ∗
, 2006
"... Partial differential equations are used to describe physical phenomena in many science and engineering fields. Finite differencing methods map these continuous equations into discrete space so that they may be solved on computers. CoArray Fortran provides the means for implementing such solution me ..."
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Cited by 7 (0 self)
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Partial differential equations are used to describe physical phenomena in many science and engineering fields. Finite differencing methods map these continuous equations into discrete space so that they may be solved on computers. CoArray Fortran provides the means for implementing such solution
Finite differencing of logical formulas for static analysis
 IN PROC. 12TH ESOP
, 2003
"... This paper concerns mechanisms for maintaining the value of an instrumentationpredicate (a.k.a. derived predicate or view), defined via a logical formula over core predicates, in response to changes in the values of the core predicates. It presents an algorithm fortransforming the instrumentation p ..."
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Cited by 37 (17 self)
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This paper concerns mechanisms for maintaining the value of an instrumentationpredicate (a.k.a. derived predicate or view), defined via a logical formula over core predicates, in response to changes in the values of the core predicates. It presents an algorithm fortransforming the instrumentation predicate's defining formula into a predicatemaintenance formula that captures what the instrumentation predicate's new value should be.This technique applies to programanalysis problems in which the semantics of statements is expressed using logical formulas that describe changes to corepredicate values,and provides a way to reflect those changes in the values of the instrumentation predicates.
ON ONE DIMENSIONAL GEOSTROPHIC ADJUSTMENT WITH FINITE DIFFERENCING ‘I
, 1977
"... i~ q. NPS—53Zh77O4l NAVAL POSTORADUAT E SCHOOL ..."
EVOLVING RELATIVISTIC FLUID SPACETIMES USING PSEUDOSPECTRAL METHODS AND FINITE DIFFERENCING
, 2007
"... We present a new code for solving the coupled Einsteinhydrodynamics equations to evolve relativistic, selfgravitating fluids. The Einstein field equations are solved on one grid using pseudospectral methods, while the fluids are evolved on another grid by finite differencing. We discuss implementa ..."
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We present a new code for solving the coupled Einsteinhydrodynamics equations to evolve relativistic, selfgravitating fluids. The Einstein field equations are solved on one grid using pseudospectral methods, while the fluids are evolved on another grid by finite differencing. We discuss
Automated and parallel code generation for finitedifferencing stencils with arbitrary data types
 Computer Science, Massey University
, 2009
"... FiniteDi↵erencing and other regular and direct approaches to solving partial di↵erential equations (PDEs) are methods that fit well on dataparallel computer systems. These problems continue to arise in many application areas of computational science and engineering but still o↵er some programming ..."
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Cited by 3 (3 self)
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FiniteDi↵erencing and other regular and direct approaches to solving partial di↵erential equations (PDEs) are methods that fit well on dataparallel computer systems. These problems continue to arise in many application areas of computational science and engineering but still o↵er some programming
AutoGeneration of Parallel FiniteDifferencing Code for MPI, TBB and CUDA
"... Abstract—Finitedifference methods can be useful for solving certain partial differential equations (PDEs) in the time domain. Compiler technologies can be used to parse an application domain specific representation of these PDEs and build an abstract representation of both the equation and the des ..."
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Abstract—Finitedifference methods can be useful for solving certain partial differential equations (PDEs) in the time domain. Compiler technologies can be used to parse an application domain specific representation of these PDEs and build an abstract representation of both the equation
QuasiOrthogonality FiniteDifferencing: Elementary Approach to Geometric Discrepancy
, 1993
"... It is possible to place n points in dspace so that, given any twocoloring of the points, there exists a halfspace within which one color dominates the other by as much as cn 1=201=2d , for some constant c ? 0. This result was proven in a slightly weaker form by Beck and the bound was later tighte ..."
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It is possible to place n points in dspace so that, given any twocoloring of the points, there exists a halfspace within which one color dominates the other by as much as cn 1=201=2d , for some constant c ? 0. This result was proven in a slightly weaker form by Beck and the bound was later tightened by Alexander. It was shown to be quasioptimal by Matousek, Welzl, and Wernisch. The lower bound proofs are highly technical and do not provide much intuitive insight into the "largediscrepancy" phenomenon. We develop a proof technique which allows us to rederive the same lower bound in a much simpler fashion. We give a probabilistic interpretation of the result and we discuss the connection of our method to Beck's Fourier transform approach. We also provide a quasioptimal lower bound on the discrepancy of fixedsize rotated boxes, which significantly improves the previous bound. 1 Introduction The Fourier transform, and more specifically, the classical (e.g., Fej'er, Gauss) summabilit...
Results 1  10
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274