Coordinate Free Programming of Computational Fluid Dynamics Problems

Grant, P.W.; Haveraaen, Magne; Webster, M.F.

doi:10.1155/2000/419840

Cited by 15 publications

(11 citation statements)

References 24 publications

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“…The Sophus approach is more properly called coordinate-free numerics [14]. A fully worked example of conventional vs. coordinate-free programming of a computational fluid dynamics problem (wire coating for Newtonian and non-Newtonian flows) is given in [12].…”

Section: Introductionmentioning

confidence: 99%

An Algebraic Programming Style for Numerical Software and Its Optimization

Dinesh¹,

Haveraaen

Heering

2000

Scientific Programming

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The abstract mathematical theory of partial differential equations (PDEs) is formulated in terms of manifolds, scalar fields, tensors, and the like, but these algebraic structures are hardly recognizable in actual PDE solvers. The general aim of the Sophus programming style is to bridge the gap between theory and practice in the domain of PDE solvers. Its main ingredients are a library of abstract datatypes corresponding to the algebraic structures used in the mathematical theory and an algebraic expression style similar to the expression style used in the mathematical theory. Because of its emphasis on abstract datatypes, Sophus is most naturally combined with object-oriented languages or other languages supporting abstract datatypes. The resulting source code patterns are beyond the scope of current compiler optimizations, but are sufficiently specific for a dedicated source-to-source optimizer. The limited, domain-specific, character of Sophus is the key to success here. This kind of optimization has been tested on computationally intensive Sophus style code with promising results. The general approach may be useful for other styles and in other application domains as well.

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Section: Introductionmentioning

confidence: 99%

An Algebraic Programming Style for Numerical Software and Its Optimization

Dinesh¹,

Haveraaen

Heering

2000

Scientific Programming

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“…Coordinate-free numerics [10,14] is a high-level approach to writing solvers for PDEs. Solvers are written using highlevel operators on abstract tensors.…”

Section: Pde Solver Test-casementioning

confidence: 99%

Finite difference methods fengshui: alignment through a mathematics of arrays

Chetioui

Mullin

Abusdal

et al. 2019

Proceedings of the 6th ACM SIGPLAN International Workshop on Libraries, Languages and Compilers for Array Programming

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Numerous scientific-computational domains make use of array data. The core computing of the numerical methods and the algorithms involved is related to multi-dimensional array manipulation. Memory layout and the access patterns of that data are crucial to the optimal performance of the array-based computations. As we move towards exascale computing, writing portable code for efficient data parallel computations is increasingly requiring an abstract productive working environment. To that end, we present the design of a framework for optimizing scientific array-based computations, building a case study for a Partial Differential Equations solver. By embedding the Mathematics of Arrays formalism in the Magnolia programming language, we assemble a software stack capable of abstracting the continuous high-level application layer from the discrete formulation of the collective array-based numerical methods and algorithms and the final detailed low-level code. The case study lays the groundwork for achieving optimized memory layout and efficient computations while preserving a stable abstraction layer independent of underlying algorithms and changes in the architecture.CCS Concepts • Software and its engineering → Software design engineering;

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“…CFP was first implemented in the context of seismic wave simulation [3] by Haveraaen et al and Grant et al [4] presented CFP for computational fluid dynamics applications. These abstractions were implemented in C++, relying on the language's template mechanism to achieve multiple levels of reuse.…”

Section: Related Workmentioning

confidence: 99%

High-performance design patterns for modern Fortran

Haveraaen

Morris

Rouson

2013

Proceedings of the 1st International Workshop on Software Engineering for High Performance Computing in Computational Science A

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This paper presents ideas for using coordinate-free numerics in modern Fortran to achieve code flexibility in the partial differential equation (PDE) domain. We also show how Fortran, over the last few decades, has changed to become a language well-suited for state-of-the-art software development. Fortran's new coarray distributed data structure, the language's class mechanism, and its side-effect-free, pure procedure capability provide the scaffolding on which we implement HPC software. These features empower compilers to organize parallel computations with efficient communication. We present some programming patterns that support asynchronous evaluation of expressions comprised of parallel operations on distributed data. We implemented these patterns using coarrays and the message passing interface (MPI). We compared the codes' complexity and performance. The MPI code is much more complex and depends on external libraries. The MPI code on Cray hardware using the Cray compiler is 1.5-2 times faster than the coarray code on the same hardware. The Intel compiler implements coarrays atop Intel's MPI library with the result apparently being 2-2.5 times slower than manually coded MPI despite exhibiting nearly linear scaling efficiency. As compilers mature and further improvements to coarrays comes in Fortran 2015, we expect this performance gap to narrow.

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Coordinate Free Programming of Computational Fluid Dynamics Problems

Cited by 15 publications

References 24 publications

An Algebraic Programming Style for Numerical Software and Its Optimization

An Algebraic Programming Style for Numerical Software and Its Optimization

Finite difference methods fengshui: alignment through a mathematics of arrays

High-performance design patterns for modern Fortran

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