An experimental performance analysis for the rate of convergence of collocation on general domains
Mo Mu, John R. Rice · Numerical Methods for Partial Differential Equations · 1989
Abstract This paper presents an experimental performance analysis for the rate of convergence of collocation on general domains using a bicubic Hermite basis. Twenty domains are selected for the experiment from the population of PDEs on nonrectangular domains found in Realistic PDE Solutions for Non‐rectangular Domains (C. J. Ribbens and J. R. Rice, CSD‐TR 639, Department of Computer Sciences, Purdue University, 1986), including one rectangle for comparison. The result shows that the convergence of the ELLPACK module COLLOCATION behaves as O(h4) on all 19 of the nonrectangular domains. This set includes a large variety of nonrectangular domains (only two have reentrant corners). We conclude that, with very high probability, this collocation module has O(h4) convergence on general domains. The experiment is made by using the Performance Evaluation System (PES) of ELLPACK, which includes the population of PDEs on nonrectangular domains. Several performance analysis tools are used to analyze the rate of convergence, the most informative is a visual examination of the convergence behavior.