Semiconductor Analysis Using Finite Elements—Part I: Computational Aspects

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.