Computational strategies for the solution of large nonlinear problems via quasi-newton methods

The usefulness of quasi-Newton methods for the solution of nonlinear systems of equations is demonstrated. After a review of the Newton iterative method, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems of equations such as those issued from spatial discretization of continua by finite elements. The numerical examples presented comprise static and dynamic analyses of geometrical, material and combined nonlinear structural problems and a model fluid flow problem with different levels of nonlinearity. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present studies, it can be concluded that computational costs for the solution of large nonlinear systems of equations can be reduced drastically by using convenient quasi-Newton updates or by adequate combined Newton/quasi-Newton strategies

Nonlinear structural dynamics via Newton and quasi-Newton methods

This paper is an attempt to compare Newton and quasi-Newton methods in nonlinear structural dynamics. After a review of the classical iterative methods, several quasi-Newton updates are presented and tested. Special attention is devoted to the solution of large sparse systems for which two original procedures are described: a substructure correction and a vectorial correction. The numerical examples presented include the dynamic analyses of geometrical, material and combined nonlinearities. All the results are assorted with a complete discussion of the different methods used, of the convergence rates and of the associated computer costs. From the present results, Newton's methods appear to exhibit the best convergence rates when an efficient computational strategy is adopted. Nevertheless computational costs for the solution of large systems can be reduced drastically by using convenient quasi-Newton updates

A new simulation algorithm for lattice QCD with dynamical quarks

A previously introduced multi-boson technique for the simulation of QCD with dynamical quarks is described and some results of first test runs on a $6^3\times12$ lattice with Wilson quarks and gauge group SU(2) are reported.Comment: 7 pages, postscript file (166 KB

Electronic Structures of Quantum Dots and the Ultimate Resolution of Integers

The orbital angular momentum L as an integer can be ultimately factorized as a product of prime numbers. We show here a close relation between the resolution of L and the classification of quantum states of an N-electron 2-dimensional system. In this scheme, the states are in essence classified into different types according to the m(k)-accessibility, namely the ability to get access to symmetric geometric configurations. The m(k)-accessibility is an universal concept underlying all kinds of 2-dimensional systems with a center. Numerical calculations have been performed to reveal the electronic structures of the states of the dots with 9 and 19 electrons,respectively. This paper supports the Laughlin wave finction and the composite fermion model from the aspect of symmetry.Comment: Two figure

The place of strategic environmental assessment in the privatised electricity industry

The private sector has given relatively little attention to the emergence of strategic environmental assessment (SEA); even recently privatised utilities, where SEA might be deemed particularly appropriate, and whose activities are likely to fall within the scope of the European Union SEA Directive, have shown less interest than might be expected. However, the global trend towards the privatisation of state-owned enterprises makes the adaptation of SEA towards these industries all the more pressing. This paper addresses the place that SEA might take within the electricity sector, taking the privatised UK electricity industry as an example. Particular challenges are posed by the radical restructuring of the industry, designed to introduce competitive behaviour, making the development of comprehensive SEA processes problematic, and requiring SEA to be placed in the context of corporate environmental policy and objectives.</p

Nonlinear Flight Dynamics of Very Flexible Aircraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77147/1/AIAA-27606-989.pd