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A Hybrid Substructuring Method and an Adaptive Refinement Scheme for the Distributed Solution of Three-Dimensional Structural Problems
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Abstract
A saddle-point variational principle is constructed to derive a hybrid substructuring method for the parallel solution of three-dimensional structural mechanics problems. A given mesh is partitioned into disconnected submeshes, and an incomplete solution for the displacement field is first evaluated via a direct method. Next, intersubdomain field continuity is enforced via discrete, polynomial, and/or piece-wise polynomial Lagrange multipliers. The proposed methodology is intrinsically parallel and offers attractive features for distributed memory multiprocessors. A combined r - h adaptive refinement procedure is also developed within the context of this hybrid substructuring method. Its basic features include an element-level error indicator that is based on a parametrized variational principle, a permanent load balancing, and an easily programmable interface gluing. The overall computational approach is applied to the structural analysis of the cabin of a launch vehicle on the iPSC/860. Numerical and performance results are reported and discussed in details. They demonstrate the potential of the methodology for the parallel solution of realistic structural mechanics problems.
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Farhat, C., Felippa, C., and Militello, C., "A Hybrid Substructuring Method and an Adaptive Refinement Scheme for the Distributed Solution of Three-Dimensional Structural Problems," SAE Technical Paper 921082, 1992, https://doi.org/10.4271/921082.Also In
References
- Agarwal T. K. Storaasli O. O. Nguyen D. T. “A Parallel-Vector Algorithm for Rapid Structural Analysis on High-Performance Computers,” AIAA / ASME / ASCE / AHS 31th Structures , Structural Dynamics and Materials Conference Long Beach, California April 2-4 1990
- Poole E. Overman A. “The Solution of Linear Systems of Equations with a Structural Analysis Code on the NAS CRAY-2,” NASA Contractor Report 4159 1988
- Farhat C. “Redesigning the Skyline Solver for Parallel/Vector Supercomputers,” International Journal of High Speed Computing 2 3 223 238 1990
- Farhat C. “Which Parallel Finite Element Algorithm for Which Architecture and Which Problem,” Engineering Computations 7 3 185 195 1990
- Bramble J. H. Pasciak J. E. Schatz A. H. Preconditioners for interface problems on mesh domains Dept. Math. Cornell Univ. Ithaca, NY 1984
- Babuska I. “The p and h - p Versions of the Finite Element Method. The State of the Art,” Ins. for Physical Sciences and Technology Note BN-1156 Univ. of Maryland 1986
- Kron G. “A Set of Principles to Interconnect the Solutions of Physical Systems” J. Applied Physics 24 8 965 980 1953
- Farhat C. Geradin M. “Using a Reduced Number of Lagrange Multipliers for Assembling Parallel Incomplete Field Finite Element Approximations,” Comp. Meth. Appl. Mech. Eng. (in press)
- Farhat C. “A Saddle-Point Principle Domain Decomposition Method for the Solution of Solid Mechanics Problems,” Proc. SIAM Conference on Domain Decomposition Methods for Partial Differential Equations 1991
- Farhat C. Roux F. X. “A Method of Finite Element Tearing and Interconnecting and its Parallel Solution Algorithm,” Int. J. Num. Meth. Eng. 32 1205 1227 1991
- Roux F. X. “Dual and spectral properties of Schur and saddle point domain decomposition methods,” Proc. SIAM Conference on Domain Decomposition Methods for Partial Differential Equations 1991
- Gill P. E. Murray W. “Numerical methods for constrained optimization,” Gill P. E. Murray W. Academic Press London 132 135 1974
- Thompson J. F. Warsi Z. U. Wayne C. A. “Numerical Grid Generation: Foundations and Applications,” North Holland New York 1985
- Diaz A. R. Kikuchi N. Taylor J. E. “A Method of Grid Optimization for Finite Element Methods,” Comp. Meth. Appl. Mech. Eng. 41 1 453 474 1983
- Winslow A. M. -The Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform Triangular Mesh,” J. Comp. Physics 2 149 172 1967
- Winslow A. M. “Adaptive Mesh Zoning by the Equipotential Method,” Report UCID-19062 Lawrence Livermore Research Laboratories CA 1981
- Militello C. “Application of Parametrized Variational Principles in the Finite Element Method,” University of Colorado Boulder 1991
- Felippaa C. Militello C. “Variational Formulation of High Performance Finite Elements: Parametrized Variational Principles,” Computers & Structures 36 1 11 1990
- Militello C. Felippa C. “The First ANDES Elements: 9-dof Plate Bending Triangles,” Comp. Meth. Appl. Mech. Eng. 93 217 246 1991
- Flügge W. Stresses in Shells Springer-Verlag Berlin 1962
- Koiter W. T. “A Spherical Shell Under Point Loads at its Poles,” Progress in Applied Mechanics: The Prager Anniversary Volume Macmillan New York 1963
- Farhat C. “A Simple and Efficient Automatic FEM Domain Decomposer,” Computers & Structures 28 5 579 602 1988
- Farhat C. “On the Mapping of Massively Parallel Processors Onto Finite Element Graphs,” Computers & Structures 32 2 347 354 1989
- Farhat C. Wilson E. “A Parallel Active Column Equation Solver,” Computers & Structures 28 4 289 304 1988