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  • 1
    Electronic Resource
    Electronic Resource
    Data structures and algorithms for the finite element method on a data parallel supercomputer (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 881-908 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article describes a formulation of the finite element method and its implementation on a data parallel computing system. The Connection Machine® system, CM-2, has been used as the model architecture. Data structures, storage requirements, communication and parallel arithmetic complexity are analysed in detail for the cases when a processor represents an unassembled finite element and when a processor is assigned to an unassembled nodal point. Data parallel algorithms for the grid generation, the evaluation of the elemental stiffness matrices and for the iterative solution of the linear system are presented. The algorithm for evaluating the elemental stiffness matrices computes the matrix elements concurrently without communication. This concurrency is in addition to the inherent parallelism present among different finite elements. A conjugate gradient solver with diagonal pre-conditioner is used for the solution of the resulting linear system. Results from an implementation of the three-dimensional finite element method based on Lagrange elements are reported. For single-precision floating-point operations, the measured peak performance is approximately 2·4 G flops s-1 for evaluating the elemental stiffness matrices and approximately 850 M flops s-1 for the conjugate gradient solver. On a Connection Machine system with 16K physical processors, the time per conjugate gradient iteration for an application with 400 000 degrees of freedom is approximately 0·13 s for double-precision floating-point operations.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290414
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    An adaptive descent method for non-linear viscoplasticity (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1031-1054 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A forming model based on a viscoplastic flow formulation is derived which includes the effects of small elastic strains. A significant feature of the formulation is its reliance on the dominant inelastic material characteristics in the formation of the stiffness matrix for large strain problems. The resultant non-linear system of equations is solved by an adaptive descent method which combines the rapid convergence of Newton's method near the solution with the robustness of a method of successive approximations. The use of the adaptive descent method effectively extends the viscoplastic flow formulations into the nearly rate-insensitive range of behaviours exhibited, for example, by metals at low temperature, where slow convergence of the non-linear solution algorithm has traditionally hampered their use.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310602
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Experience with the conjugate gradient method for stress analysis on a data parallel supercomputer (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 523-546 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The storage requirements and performance consequences of a few different data parallel implementations of the finite element method for domains discretized by three-dimensional brick elements are reviewed. Letting a processor represent a nodal point per unassembled finite element yields a concurrency that may be one to two orders of magnitude higher for common elements than if a processor represents an unassembled finite element. The former representation also allows for higher order elements with a limited amount of storage per processor. A totally parallel stiffness matrix generation algorithm is presented. The equilibrium equations are solved by a conjugate gradient method with diagonal scaling. The results from several simulations designed to show the dependence of the number of iterations to convergence upon the Poisson ratio, the finite element discretization and the element order are reported. The domain was discretized by three-dimensional Lagrange elements in all cases. The number of iterations to convergence increases with the Poisson ratio. Increasing the number of elements in one special dimension increases the number of iterations to convergence, linearly. Increasing the element order p in one spatial dimension increases the number of iterations to convergence as pα, where α is 1·4-1·5 for the model problems.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270307
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    A case study in parallel computation: Viscous flow around an ONERA M6 wing (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 877-884 
    Details
    ISSN: 0271-2091
    Keywords: ONERA M6 wing ; parallel computing ; viscous flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: We examine the solution of a practical engineering problem on a parallel computer. The problem involves the steady laminar viscous flow about an ONERA M6 wing and the computer is a 64-processing-node Connection Machine CM-5E. We show that efficient domain decomposition procedures lead to a balanced load on the processors and low communication times. The net result is that solutions can be attained in roughly 20 min elapsed time for a 48,011-node, 266,566-element unstructured mesh. We conclude that this is sufficiently fast to support the design process.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650211008
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    Paper (German National Licenses)
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