The mesh of trees architecture for parallel computation
Hornick, Scot W.
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Permalink
https://hdl.handle.net/2142/23253
Description
Title
The mesh of trees architecture for parallel computation
Author(s)
Hornick, Scot W.
Issue Date
1989
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Computer Science
Language
eng
Abstract
This thesis considers the mesh of trees architecture as both a special-purpose and a general-purpose parallel computer. A family of special-purpose VLSI architectures for computing an ($n\sb1 \times n\sb2 \times \cdots \times n\sb{d}$)-point multidimensional DFT over $\doubz\sb{M}$, the ring of integers modulo $M$, is proposed. Using the two-dimensional mesh of trees as a component, these architectures achieve optimal VLSI area $A$ = $\Theta((N\sp2\log\sp{2}M)/T\sp2)$ for any given computation time $T\ \epsilon$ ($\Omega(\log N),O(\sqrt{N\log M})\rbrack.$
The convergence properties of Newton's method are studied. By introducing and formalizing the notion of attunement of a linear system of equations, it is shown that Newton's method provides polylog-time solutions for a broader class of linear systems than was previously supposed. In particular, the system matrix need not be well-conditioned; all that is required is that the known vector be well-attuned to the system matrix. It is then shown that Newton's method can be implemented on a special-purpose architecture based on the three-dimensional mesh of trees. This same architecture can be used to construct the stiffness equations arising from a finite element approximation. Furthermore, it can be hybridized with a systolic array to achieve a processor-time or area-time tradeoff.
Then, in a different vein, the two-dimensional mesh of trees is studied as a general-purpose parallel computer. It is shown that this architecture can afford finer memory granularity and, thereby, reduce the memory redundancy required for deterministic P-RAM simulation. A distributed-memory, bounded-degree network model of parallel computation is proposed that allows one to take greater advantage of the potential for fine-grain memories without sacrificing other aspects of realism. The simulation scheme presented is admitted by this new model and achieves constant memory redundancy.
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