Iterative solution of the global element equations

• Published in: Computer methods in applied mechanics and engineering Vol. 35; no. 3; pp. 271 - 283
• Main Authors: Hendry, J.A., Delves, L.M., Mohamed, J.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.01.1982
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/0045-7825(82)90106-2

A previous paper [4]discussed in detail techniques for setting up the defining equations for the Global Element Method for elliptic partial differential equations, and sketched an iterative method for their solution. For a calculation in two-dimensions using M elements (with a basis of degree N - 1 in each element), operation counts of O( MN 4) were achieved for both set-up and solution phases. Timings were included demonstrating this count for the set-up, but not the solution, phase. In this paper we describe a modified and simpler version of the iterative solution scheme and report timings obtained with an exploratory implementation of the scheme. These demonstrate the rapid convergence and O( MN 4) behaviour predicted for it.