Engineering topics
Publications and source records attributed to Melosh, R..
Five direct and five iterative algorithms for finite element equations in linear equilibrium problems investigated for number of parallel computer architectures and their basic computation methods compared.
Computer architectures designed for concurrent processing are characterized by the number of processing elements, ensemble speed, random access memory, input/output routes, and modes of operation. The important attributes of processing tasks are then identified, and some processing stratagems are examined. It is shown that the greater the complexity of a given task, the wider the range of possible stratagems which can accomplish the task. For relatively simple tasks, the optimum stratagem can be found by analytical reasoning. For more complex tasks, however, optimum scheduling techniques may have to be employed for the assignment of segments of the task to the available processing elements.
A computer code, SCOPE, has been developed for predicting the computer resources required for a given analysis code, computer hardware, and structural problem. The cost of running the code is a small fraction (about 3 percent) of the cost of performing the actual analysis. However, its accuracy in predicting the CPU and I/O resources depends intrinsically on the accuracy of calibration data that must be developed once for the computer hardware and the finite element analysis code of interest. Testing of the SCOPE code on the AMDAHL 470 V/8 computer and the ELAS finite element analysis program indicated small I/O errors (3.2 percent), larger CPU errors (17.8 percent), and negligible total errors (1.5 percent).
The paper examines several parallel processing solution algorithms for finite element equations arising in linear equilibrium problems. Two basic groups of algorithms, direct and iterative, are investigated with respect to a number of parallel computer architectures and associated selection criteria. The direct algorithms include: LR-Gauss, Crout, Cholesky, Cyclic Reduction and WZ-factorization. The iterative methods examined are: Accelerated Gauss-Seidel, Surrogate Stiffness, Jacobi, Series Expansion, and Energy Monte Carlo. For real-time applications, where the object is to minimize the execution time, Cyclic Reduction appears to be best suited. This assumes a computer with an unlimited number of parallel processors. However, for computers with a limited number of parallel processors that must be used efficiently, both Gauss factorization and Jacobi-like iterative methods rank favorably.
Numerical solution of nonlinear equilibrium problems of structures by means of Newton-Raphson type iterations is reviewed. Each step of the iteration is shown to correspond to the solution of a linear problem, therefore the feasibility of the finite element method for nonlinear analysis is established. Organization and flow of data for various types of digital computers, such as single-processor/single-level memory, single-processor/two-level-memory, vector-processor/two-level-memory, and parallel-processors, with and without sub-structuring (i.e. partitioning) are given. The effect of the relative costs of computation, memory and data transfer on substructuring is shown. The idea of assigning comparable size substructures to parallel processors is exploited. Under Cholesky type factorization schemes, the efficiency of parallel processing is shown to decrease due to the occasional shared data, just as that due to the shared facilities.
Numerical procedure for structural systems analysis, discussing computer application to hydrodynamic, electric, magnetic, thermodynamic, elastostatic and elastodynamic problems
Numerical procedure for structural systems analysis, discussing computer application to hydrodynamic, electric, magnetic, thermodynamic, elastostatic and elastodynamic problems