Search

This paper addresses the role of centrality in the implementation of interior point methods. We provide theoretical arguments to justify the use of a symmetric neighbourhood, and translate them into computational practice leading to a new insight into the role of re-centering in the implementation of interior point methods. Second-order correctors, such as Mehrotra's predictor-corrector, can occasionally fail: we derive a remedy to such difficulties from a new interpretation of multiple centrality correctors. Through extensive numerical experience we show that the proposed centrality correcting scheme leads to noteworthy savings over second-order predictor-corrector technique and previous implementations of multiple centrality correctors.

In aeronautical industry numerical flow simulation has become a key element in the aerodynamic design process. However, in order to meet the ambitious goals for air traffic of the next decades, significant investment in enhancing the capabilities and tools of numerical simulations in various aspects is required. Within the 7th European Research Framework Programme, the collaborative target research project IDIHOM was initiated. The overall objective of this project was to enhance and mature adaptive high-order simulation methods for large-scale applications. Compared to its low-order counterparts, high-order methods have shown large potential to either increase the predictive accuracy related to the descretization error at given costs or to significantly reduce computational expenses for a prescribed accuracy. The IDIHOM project was driven by a top-down approach, in which dedicated enhancements and improvements of the complete high-order simulation framework, including grid generation, flow solver and visualization, were led by a suite of underlying and challenging test cases. The project gathered 21 partners from industry, research organizations and universities with well-proven expertise in high-order methods. It started end October 2010 and finished March 2014. This paper presents the achievements of the project and highlights strenghts, weaknesses and perspectives of higher-order methods for aerodynamic applications.

The extended framework of Hamilton’s principle and the mixed convolved action principle provide new rigorous weak variational formalism for a broad range of initial boundary value problems in mathematical physics and mechanics. In this paper, their potential when adopting temporally higher order approximations is investigated. The classical single-degree-of-freedom dynamical systems are primarily considered to validate and to investigate the performance of the numerical algorithms developed from both formulations. For the undamped system, all the algorithms are symplectic and unconditionally stable with respect to the time step. For the damped system, they are shown to be accurate with good convergence characteristics.

Parallelization of time-consuming volume integrations in the matrix filling is performed using OpenMP to provide a smooth transition of a higher order finite element method (FEM) code for electromagnetic analysis to the multi-core hardware architecture. In the process, the carefully constructed original computational scheme suited to maximally avoid the redundant computations in the higher order FEM is not affected. The results, in analysis of an electrically large dielectric scatterer, demonstrate acceleration of up to 2.28 times in a four-thread architecture. 20th Telecommunications Forum, Proceedings, Nov 20-22, 2012, Belgrade, Serbia