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On the accuracy of some domain‐by‐domain algorithms for parallel processing of transient structural dynamics
Author(s) -
Hajjar Jerome F.,
Abel John F.
Publication year - 1989
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620280811
Subject(s) - algorithm , transient (computer programming) , computer science , domain (mathematical analysis) , finite element method , time domain , simple (philosophy) , frame (networking) , mathematics , engineering , mathematical analysis , structural engineering , telecommunications , philosophy , epistemology , computer vision , operating system
Two domain‐by‐domain algorithms, suitable for coarse‐grained parallel processing analysis of the transient structural dynamics equation, are investigated for accuracy. The application under specific consideration is the analysis of three‐dimensional framed structures subjected to time‐varying loading. The domain‐by‐domain approaches attempt to include the advantageous aspects of both conditionally stable explicit algorithms, which require no simultaneous solution of equations and employ simple communication, and unconditionally stable implicit algorithms, which permit large time steps. The alternating group explicit algorithm is developed for finite element analysis, and its accuracy is investigated for a linear formulation. The group implicit algorithm is extended to non‐linear finite element analysis, and its accuracy is investigated for the frame dynamics application. Both algorithms are shown to provide inadequate accuracy for practical time step sizes.