## Declarative Solutions to Partitioned-Grid Problems (1998)

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### BibTeX

@TECHREPORT{Etalle98declarativesolutions,

author = {Ro Etalle and Sandro Etalle and Pieter H. Hartel and Pieter H. Hartel and William G. Vree and Willem G. Vree},

title = {Declarative Solutions to Partitioned-Grid Problems},

institution = {},

year = {1998}

}

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### Abstract

The problem of partitioning grid-based applications for parallel computing can be solved easily and intuitively in a logic programming language such as Prolog, using only the single assignment property of the logic variable, and not the backtracking.

### Citations

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Citation Context ...d efficiency is achieved only if the compiler translates the array comprehensions properly. The present Id compiler has this capability, but many of its competitors (e.g. the Glasgow Haskell compiler =-=[24]-=-) do not. To investigate how array comprehensions and list comprehensions could be embedded into Prolog would be an interesting area of future work. 6 Conclusions Iterative grid-based calculations ari... |

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Citation Context ...nto a functional program proceeds in four stages. Each transformation stage will now be discussed in detail in subsequent sections. We will use some primitives from the languages Tale [4] and Haskell =-=[17]-=-. Their type signatures, along with those of a few standard functions are shown below. array ff j : : : matrix ff j : : : descr j ((num; num); (num; num)) get descr :: matrix ff ! descr tabulate :: (n... |

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Citation Context ...tional programming, either side by side, or in an integrated fashion, is by no means a novel idea. A large amount of work has been done on the integration of functional and logic languages. See Hanus =-=[11]-=- for a recent comprehensive survey from the point of view of admitting a general notion of equality in logic programming. An early survey of the dual approach (integrating logic variables into a funct... |

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Citation Context ...ide these new values. The implementation lr grid 0 below describes the process more precisely, assuming that the size of the grid to be created is m \Theta n. Here we are using an array comprehension =-=[1]-=-. This construct has a semantics similar to that of the for-loop in an imperative programming language. The function array 2D below takes as its arguments a 2-dimensional descriptor and a list of pair... |

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Citation Context ...er equations [27]. The solution method is based on domain decomposition of nonoverlapping boxes; it also computes exact solutions. We have developed a number of ways to effect the exchange of borders =-=[13, 31, 32]-=-. In the present paper we will again use the shallow water equations as a case study. Section 2 describes the partitioning of a grid and the associated problems involved in the exchange of borders. Se... |

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Citation Context ...Prolog program into a functional program proceeds in four stages. Each transformation stage will now be discussed in detail in subsequent sections. We will use some primitives from the languages Tale =-=[4]-=- and Haskell [17]. Their type signatures, along with those of a few standard functions are shown below. array ff j : : : matrix ff j : : : descr j ((num; num); (num; num)) get descr :: matrix ff ! des... |

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Citation Context ...er equations [27]. The solution method is based on domain decomposition of nonoverlapping boxes; it also computes exact solutions. We have developed a number of ways to effect the exchange of borders =-=[13, 31, 32]-=-. In the present paper we will again use the shallow water equations as a case study. Section 2 describes the partitioning of a grid and the associated problems involved in the exchange of borders. Se... |

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Citation Context ...ures in lazy functional languages, but it is unlikely that no such papers exist. The use of logic variables to solve problems involved in the exchange of borders is mentioned by Pingali and Ekanadham =-=[25]-=-. Their paper, however, is concerned with generalised logic variables (accumulators) and the integration of accumulators in a functional language. Knott [20] uses both Miranda and Prolog for animating... |

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Citation Context ...ticity and quantum mechanics [19]. Solving sparse symmetric linear systems that arise from discretization of elliptic partial differential equations is one of the main problems in computation science =-=[21]-=-. All methods for solving partial differential equations give rise to the same kind of computational structure: iterative grid-based calculations. An important property of these calculations is locali... |

2 |
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Citation Context .... The group of Arvind at MIT has worked for many years on implementations of functional programming languages with special emphasis on supporting scientific applications. The languages Id [22] and Ph =-=[23]-=- provide special data structures, such as the I-structure [3] and the M-structure [5]. The latter allows data values to be replaced by new data values. The more restricted I-structure allows component... |

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1 |
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Citation Context ...ng partial differential equations on parallel computers case studies are presented concerning wave propagation, petrol engineering, aerodynamics, discrete simulation, elasticity and quantum mechanics =-=[19]-=-. Solving sparse symmetric linear systems that arise from discretization of elliptic partial differential equations is one of the main problems in computation science [21]. All methods for solving par... |