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A Family of Concurrent Algorithms for Transient Finite Element Solutions

by B. Nour-Omid, Lockheed Palo Alto Research Lab, United States,
M.. Ortiz, Lockheed Palo Alto Research Lab, United States,



Document Type: Proceeding Paper

Part of: Computer Utilization in Structural Engineering

Abstract:

We derive a family of methods for solving the equations of motion arising in structural dynamics which makes effective use of the architecture of concurrent computers. The algorithm is obtained by applying a splitting scheme to the modified equations of motion for a group of substructures and the associated compatibility constraints. Each substructure is processed over a time step independently of the others. Thus, high levels of concurrency can be achieved during this phase of the analysis. The solution of the complete system is constructed by 'gluing' the solutions for the substructures. This involves averaging the solutions at the interfaces between the subsystems. This averaging scheme is derived by enforcing the compatibility condition between the substructures. The resulting two parameter algorithm is shown to be equivalent to the concurrent algorithm and therefore is unconditionally stable for linear analysis.

Subject Headings: Finite element method | Equations of motion | Algorithms | Substructures | Computer programming | Linear analysis | Dynamic structural analysis

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