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IBM Journal of Research and Development  
Volume 25, Number 4, Page 232 (1981)
Finite Element Analysis
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Semiconductor Analysis Using Finite Elements—Part I: Computational Aspects

by G. D. Hachtel, 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.
Related Subjects: Computational methods; Mathematics (applied); Models and modeling; Physics; Semiconductor technology