J. W. Neuberger

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We describe a Sobolev gradient method for finding minima of the Ginzburg–Landau functional for superconductivity. This method leads to a particularly simple algorithm which avoids consideration of the nonlinear boundary conditions associated with the Ginzburg–Landau equations. 1. Introduction. There is considerable current interest in finding minima of(More)
A common problem in physics and engineering is the calculation of the minima of energy functionals. The theory of Sobolev gradients provides an efficient method for seeking the critical points of such a functional. We apply the method to functionals describing coarse-grained Ginzburg-Landau models commonly used in pattern formation and ordering processes.