A Two-Step Certified Reduced Basis Method

In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization. The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach.United States. Air Force Office of Scientific Research (AFOSR Grant number FA9550-07-1-0425)United States. Department of Defense. Office of the Secretary of Defense (OSD/AFOSR Grant number FA9550-09-1-0613)Norwegian University of Science and Technolog

Model Order Reduction in Fluid Dynamics: Challenges and Perspectives

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities — which are mainly related either to nonlinear convection terms and/or some geometric variability — that often cannot be treated by simple linearization. Additional difficulties arise when attempting model reduction of unsteady flows, especially when long-term transient behavior needs to be accurately predicted using reduced order models and more complex features, such as turbulence or multiphysics phenomena, have to be taken into consideration. We first discuss some general principles that apply to many parametric model order reduction problems, then we apply them on steady and unsteady viscous flows modelled by the incompressible Navier-Stokes equations. We address questions of inf-sup stability, certification through error estimation, computational issues and — in the unsteady case — long-time stability of the reduced model. Moreover, we provide an extensive list of literature references

Control of glyphosate resistant hairy fleabane (Conyza bonariensis) with dicamba and 2,4-D Controle de buva (Conyza bonariensis) resistente ao glyphosate com dicamba e 2,4-D

Auxyn type herbicides such as dicamba and 2,4-D are alternative herbicides that can be used to control glyphosate-resistant hairy fleabane. With the forthcoming possibility of releasing dicamba-resistant and 2,4-D-resistant crops, use of these growth regulator herbicides will likely be an alternative that can be applied to the control of glyphosate resistant hairy fleabane (Conyza bonariensis). The objective of this research was to model the efficacy, through dose-response curves, of glyphosate, 2,4-D, isolated dicamba and glyphosatedicamba combinations to control a brazilian hairy fleabane population resistant to glyphosate. The greenhouse dose-response studies were conducted as a completely randomized experimental design, and the rates used for dose response curve construction were 0, 120, 240, 480, 720 and 960 g a.i. ha-1 for 2,4-D, dicamba and the dicamba combination, with glyphosate at 540 g a.e. ha-1. The rates for glyphosate alone were 0, 180, 360, 540, 720 and 960 g a.e. ha-1. Herbicides were applied when the plants were in a vegetative stage with 10 to 12 leaves and height between 12 and 15 cm. Hairy fleabane had low sensitivity to glyphosate, with poor control even at the 960 g a.e. ha-1 rate. Dicamba and 2,4-D were effective in controlling the studied hairy fleabane. Hairy fleabane responds differently to 2,4-D and dicamba. The combination of glyphosate and dicamba was not antagonistic to hairy fleabane control, and glyphosate may cause an additive effect on the control, despite the population resistance.<br>Os herbicidas mimetizadores de auxinas como dicamba e 2,4-D são alternativas para o controle de buva resistente ao glyphosate. Com a possível futura liberação comercial de culturas resistentes ao dicamba e 2,4-D, a aplicação destes herbicidas reguladores de crescimento será uma provável alternativa de controle de buva resistente ao glyphosate. O objetivo desta pesquisa foi modelar por meio de curvas de dose-resposta a eficácia do dicamba e 2,4-D isolados e dicamba em associação com glyphosate para controle de uma população de buva resistente. Um estudo de doseresposta em casa de vegetação foi conduzido em delineamento experimental inteiramente casualizado, sendo que as doses utilizadas para a construção das curvas de dose-resposta foram de 0, 120, 240, 480, 720 e 960 g i.a. ha-1de para o dicamba e o 2,4-D isolados e dicamba associado com 540 g e.a. ha-1 de glyphosate. As doses utilizadas para o glyphosate isolado foram de 0, 180, 360, 540, 720 e 960 g e.a. ha-1. Os tratamentos herbicidas foram aplicados quando asplantas estavam no estádio vegetativo de 10 a 12 folhas e altura entre 12 e 15 cm. A buva apresentou baixa sensibilidade ao glyphosate, pois não foi controlada mesmo na dose de 960 g e.a. ha-1 de glyphosate. O dicamba e o 2,4-D foram eficazes no controle da população de buva estudada. A buva responde de forma diferenciada ao 2,4-D e dicamba e será importante determinaras doses apropriadas de cada herbicida para controle de buva resistente ao glyphosate em condições de campo. A associação de glyphosate e dicamba não foi antagônica no controle da buva e o glyphosate pode causar um efeito aditivo no controle, apesar da resistência da população