Partitioning Regular Domains on Modern Parallel Computers

This monograph describes various methods for solving deformation problems of particulate solids, taking the reader from analytical to computational methods. The book is the first to present the topic of linear elasticity in mathematical terms that will be familiar to anyone with a grounding in fluid mechanics. It incorporates the latest advances in computational algorithms for elliptic partial differential equations, and provides the groundwork for simulations on high performance parallel computers. Numerous exercises complement the theoretical discussions, and a related set of self-documented programs is available to readers with Internet access. The work will be of interest to advanced students and practicing researchers in mechanical engineering, chemical engineering, applied physics, computational methods, and developers of numerical modeling software.

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Practical Wavelet Tree Construction

Journal of Experimental Algorithmics ◽

10.1145/3457197 ◽

2021 ◽

Vol 26 ◽

pp. 1-67

Author(s):

Patrick Dinklage ◽

Jonas Ellert ◽

Johannes Fischer ◽

Florian Kurpicz ◽

Marvin Löbel

Keyword(s):

Parallel Algorithms ◽

Shared Memory ◽

Distributed Memory ◽

Auxiliary Information ◽

Parallel Computers ◽

External Memory ◽

Sequential Algorithms ◽

Bottom Up ◽

Memory Efficiency ◽

Tree Construction

We present new sequential and parallel algorithms for wavelet tree construction based on a new bottom-up technique. This technique makes use of the structure of the wavelet trees—refining the characters represented in a node of the tree with increasing depth—in an opposite way, by first computing the leaves (most refined), and then propagating this information upwards to the root of the tree. We first describe new sequential algorithms, both in RAM and external memory. Based on these results, we adapt these algorithms to parallel computers, where we address both shared memory and distributed memory settings. In practice, all our algorithms outperform previous ones in both time and memory efficiency, because we can compute all auxiliary information solely based on the information we obtained from computing the leaves. Most of our algorithms are also adapted to the wavelet matrix , a variant that is particularly suited for large alphabets.

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Modeling performance of the multiscale fluid numerical solver on large-scale parallel computers

Proceedings of the 2020 4th International Conference on High Performance Compilation, Computing and Communications ◽

10.1145/3407947.3407953 ◽

2020 ◽

Author(s):

Xiao-Wei Guo ◽

Chao Li

Keyword(s):

Large Scale ◽

Parallel Computers ◽

Numerical Solver

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Using an architectural knowledge base to generate code for parallel computers

Communications of the ACM ◽

10.1145/66451.66453 ◽

1989 ◽

Vol 32 (9) ◽

pp. 1065-1072 ◽

Cited By ~ 6

Author(s):

Anthony E. Terrano ◽

Stanley M. Dunn ◽

Joseph E. Peters

Keyword(s):

Knowledge Base ◽

Parallel Computers ◽

Architectural Knowledge

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A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127493000234 ◽

1993 ◽

Vol 03 (02) ◽

pp. 293-321 ◽

Cited By ~ 1

Author(s):

JÜRGEN WEITKÄMPER

Keyword(s):

Hopf Bifurcation ◽

Dynamical Systems ◽

Cellular Automata ◽

Cellular Automaton ◽

Parallel Computers ◽

Discrete Dynamical Systems ◽

Two Dimensional ◽

Bifurcation Structure ◽

Logistic Mapping ◽

Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

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Index-Shuffle Graphs

International Journal of Foundations of Computer Science ◽

10.1142/s0129054197000197 ◽

1997 ◽

Vol 08 (03) ◽

pp. 289-304 ◽

Cited By ~ 2

Author(s):

Marc Baumslag ◽

Bojana Obrenić

Keyword(s):

Interconnection Networks ◽

Graph Embedding ◽

Theoretical Framework ◽

Parallel Computers ◽

Bounded Degree ◽

Exchange Graph ◽

Comparative Advantages ◽

On Line

Index-shuffle graphs are introduced as candidate interconnection networks for parallel computers. The comparative advantages of index-shuffle graphs over the standard bounded-degree "approximations" of the hypercube, namely butterfly-like and shuffle-like graphs, are demonstrated in the theoretical framework of graph embedding and network emulations. An N-node index-shuffle graph emulates: • an N-node shuffle-exchange graph with no slowdown, which the currently best emulations of shuffle-like graphs by hypercubes and butterflies incur a slowdown of Ω( log N). • its like-sized butterfly graph with a slowdown O( log log log N), while the currently best emulations of butterfly-like graphs by shuffle-like graphs incur a slowdown of Ω( log log N). • an N-node hypercube that executes an on-line leveled algorithm with a slowdown O( log log N), while the slowdown of currently best such emulations of the hypercube by its bounded-degree shuffle-like and butterfly-like derivatives remains Ω( log N). Our emulation is based on an embedding of an N-node hypercube into an N-node index-shuffle graph with dilation O( log log N), while the currently best embeddings of the hypercube into its bounded-degree shuffle-like and butterfly-like derivatives incur a dilation of Ω( log N).

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