Convergence Analysis of Pseudo-Transient Continuation

Abstract

. Pseudo-transient continuation (\\Psitc) is a well-known and physically motivated technique for computation of steady-state solutions of time-dependent partial differential equations. Standard globalization strategies such as line search or trust region methods often stagnate at local minima. \\Psitc succeeds in many of these cases by taking advantage of the underlying PDE structure of the problem. Though widely employed, the convergence of \\Psitc is rarely discussed. In this paper we prove convergence for a generic form of \\Psitc and illustrate it with two practical strategies. Key words. Pseudo-transient continuation, nonlinear equations, steady-state solutions, global convergence AMS subject classifications. 65H10, 65J15, 65N12, 65N22 1. Introduction. Pseudo-transient continuation (\\Psitc) is a method for computation of steadystate solutions of partial differential equations. We shall interpret the method in the context of a method-of-lines solution, in which the equation is discre...