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Semiconductor Analysis Using Finite Elements—Part I: Computational Aspects

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4 Author(s)
G. D. Hachtel ; IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA ; M. H. Mack ; R. R. O'Brien ; B. Speelpenning

We describe the computer implementation of SAFE, a general-purpose program for finite-element analysis of systems of nonlinear, nonvariational PDE. The form and nonlinearity of the PDE, as well as the domain, parameters, and boundary conditions of the problem, are user-specified. We discuss the problems of numerical integration in space and in time and describe the results of applying sparse-matrix methods to some practical problems. A method is given for unified treatment of nonstandard finite elements such as bicubic-spline and “current-continuous” elements. We give an assessment of the potential impact and reliability of general-purpose nonlinear finite-element programs. We conclude from out data that as the number of elements becomes large, sparse-matrix solutions dominate the overall operation count, even though the methods used are near-optimal for problems of moderate size.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:25 ,  Issue: 4 )