Accelerated ‘relaxation’ or direct solution? Future prospects for fem

Abstract

‘Dynamic’ or ‘viscous’ relaxation procedures have not gained much popularity in finite element analysis in which the direct (Gaussian elimination) solution dominates. Reasons for this are various—the most important being the rather slow convergence generally achieved for such procedures. However, it is possible to accelerate this quite dramatically and a method of doing so is shown in this paper. With the use of such acceleration and the inherent advantages of greatly reduced storage requirements and simplicity of programming, relaxation procedures promise an exciting possibility for the solution of large two- and three-dimensional problems in both linear and nonlinear ranges.