3 resultados para Newton-Krylov
em Repositório Científico do Instituto Politécnico de Lisboa - Portugal
Resumo:
Dissertação para obtenção do grau de Mestre em Engenharia Electrotécnica Ramo de Energia
Resumo:
Attending the British Liquid Crystal Society’s (BLCS) Annual Meeting was a formative experience in my days as a PhD student, starting way back in the 1990s. At that time, this involved travelling to (to me) exotic parts of the United Kingdom, such as Reading, Oxford or Manchester, away from Southampton where I was based. Some postdoctoral years in a different country followed, and three BLCS Meetings were missed, until in 1997 and 1998, I was able to attend again, in Southampton and Leeds, respectively. Not much had changed from my student days, the size and the format were still about the same, many of the leading characters were still around, and the closing talk would still be given by John Lydon. Well, at some point, I got myself a proper academic job on the Continent and stopped attending BLCS Annual Meetings altogether. The fond memories of my youth started to fade. Were the Meetings still on? It seemed so, as old friends and acquaintances would occasionally recount attending them, and even winning prizes at them. But, it all seemed rather remote now. Until, that is, it came to pass that the 27th BLCS Meeting would be held in Selwyn College, Cambridge, just down (or up, depending on how you look at it) the road from the Isaac Newton Institute, where I was spending part of my sabbatical leave. The opportunity to resume attendance could not be missed. A brief e-mail exchange with the organisers, and a cheque to cover the fee, duly secured this. And thus, it was with trepidation that I approached my first BLCS Annual Meeting in more than a decade.
Resumo:
The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach - Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings - When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications - Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications - A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core. Social implications - More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method. Originality/value - Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.