A partitioning strategy for nonuniform problems on multiprocessors

The partitioning of a problem on a domain with unequal work estimates in different subddomains is considered in a way that balances the work load across multiple processors. Such a problem arises for example in solving partial differential equations using an adaptive method that places extra grid points in certain subregions of the domain. A binary decomposition of the domain is used to partition it into rectangles requiring equal computational effort. The communication costs of mapping this partitioning onto different microprocessors: a mesh-connected array, a tree machine and a hypercube is then studied. The communication cost expressions can be used to determine the optimal depth of the above partitioning

Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

Optimal processor assignment for pipeline computations

The availability of large scale multitasked parallel architectures introduces the following processor assignment problem for pipelined computations. Given a set of tasks and their precedence constraints, along with their experimentally determined individual responses times for different processor sizes, find an assignment of processor to tasks. Two objectives are of interest: minimal response given a throughput requirement, and maximal throughput given a response time requirement. These assignment problems differ considerably from the classical mapping problem in which several tasks share a processor; instead, it is assumed that a large number of processors are to be assigned to a relatively small number of tasks. Efficient assignment algorithms were developed for different classes of task structures. For a p processor system and a series parallel precedence graph with n constituent tasks, an O(np2) algorithm is provided that finds the optimal assignment for the response time optimization problem; it was found that the assignment optimizing the constrained throughput in O(np2log p) time. Special cases of linear, independent, and tree graphs are also considered

System software for the finite element machine

The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested

Software Support for Irregular and Loosely Synchronous Problems

A large class of scientific and engineering applications may be classified as irregular and loosely synchronous from the perspective of parallel processing. We present a partial classification of such problems. This classification has motivated us to enhance Fortran D to provide language support for irregular, loosely synchronous problems. We present techniques for parallelization of such problems in the context of Fortran D

Software Support for Irregular and Loosely Synchronous Problems

A large class of scientific and engineering applications may be classified as irregular and loosely synchronous from the perspective of parallel processing. We present a partial classification of such problems. This classification has motivated us to enhance Fortran D to provide language support for irregular, loosely synchronous problems. We present techniques for parallelization of such problems in the context of Fortran D

Design of testbed and emulation tools

The research summarized was concerned with the design of testbed and emulation tools suitable to assist in projecting, with reasonable accuracy, the expected performance of highly concurrent computing systems on large, complete applications. Such testbed and emulation tools are intended for the eventual use of those exploring new concurrent system architectures and organizations, either as users or as designers of such systems. While a range of alternatives was considered, a software based set of hierarchical tools was chosen to provide maximum flexibility, to ease in moving to new computers as technology improves and to take advantage of the inherent reliability and availability of commercially available computing systems

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Refficientlib: an efficient load-rebalanced adaptive mesh refinement algorithm for high-performance computational physics meshes

No separate or additional fees are collected for access to or distribution of the work.In this paper we present a novel algorithm for adaptive mesh refinement in computational physics meshes in a distributed memory parallel setting. The proposed method is developed for nodally based parallel domain partitions where the nodes of the mesh belong to a single processor, whereas the elements can belong to multiple processors. Some of the main features of the algorithm presented in this paper are its capability of handling multiple types of elements in two and three dimensions (triangular, quadrilateral, tetrahedral, and hexahedral), the small amount of memory required per processor, and the parallel scalability up to thousands of processors. The presented algorithm is also capable of dealing with nonbalanced hierarchical refinement, where multirefinement level jumps are possible between neighbor elements. An algorithm for dealing with load rebalancing is also presented, which allows us to move the hierarchical data structure between processors so that load unbalancing is kept below an acceptable level at all times during the simulation. A particular feature of the proposed algorithm is that arbitrary renumbering algorithms can be used in the load rebalancing step, including both graph partitioning and space-filling renumbering algorithms. The presented algorithm is packed in the Fortran 2003 object oriented library \textttRefficientLib, whose interface calls which allow it to be used from any computational physics code are summarized. Finally, numerical experiments illustrating the performance and scalability of the algorithm are presented.Peer ReviewedPostprint (published version