A Parabolic Theory of Load Balance

Heirich, Alan and Taylor, Stephen (1993) A Parabolic Theory of Load Balance. Technical Report. California Institute of Technology. [CaltechCSTR:1993.cs-tr-93-25]

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Abstract

We derive analytical results for a dynamic load balancing algorithm modeled by the heat equation ut = V2u. The model is appropriate for quickly diffusing disturbances in a local region of a computational domain without affecting other parts of the domain. The algorithm is useful for problems in computational fluid dynamics which involve moving boundaries and adaptive grids implemented on mesh connected multicomputers. The algorithm preserves task locality and uses only local communication. Resulting load distributions approximate time asymptotic solutions of the heat equation. As a consequence it is possible to predict both the rate of convergence and the quality of the final load distribution. These predictions suggest that a typical imbalance on a multicomputer with over a million processors can be reduced by one order of magnitude after 105 arithmetic operations at each processor. For large n the time complexity to reduce the expected imbalance is effectively independent of n.

EPrint Type:	Monograph (Technical Report)
Subjects:	All Records
ID Code:	114
Deposited By:	Caltech Library System
Deposited On:	25 April 2001
Record Number:	CaltechCSTR:1993.cs-tr-93-25
Official Persistent URL:	http://resolver.caltech.edu/CaltechCSTR:1993.cs-tr-93-25
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