Search results for "CPU time"
showing 6 items of 6 documents
Approximate Lax–Wendroff discontinuous Galerkin methods for hyperbolic conservation laws
2017
Abstract The Lax–Wendroff time discretization is an alternative method to the popular total variation diminishing Runge–Kutta time discretization of discontinuous Galerkin schemes for the numerical solution of hyperbolic conservation laws. The resulting fully discrete schemes are known as LWDG and RKDG methods, respectively. Although LWDG methods are in general more compact and efficient than RKDG methods of comparable order of accuracy, the formulation of LWDG methods involves the successive computation of exact flux derivatives. This procedure allows one to construct schemes of arbitrary formal order of accuracy in space and time. A new approximation procedure avoids the computation of ex…
Branch and bound for the cutwidth minimization problem
2013
The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solu…
Modelling Aspects in Accumulative Roll Bonding Process by Explicit Finite Element Analysis
2013
Accumulative Roll-Bonding (ARB) process is a severe plastic deformation (SPD) process, capable of developing grains below 1 μm in diameter and improving mechanical properties of the material. In this study, the authors compared two different FE-codes with respect of its applicability for numerical analysis of the ARB process. Modelling this process was achieved using the explicit code for Abaqus/CAE both in 2D and 3D. The proposed model was used to assess the impact of ARB cycles on the final material properties. The numerical results in 2D and 3D were compared and contrasted. The research work presented in this paper is focused on the simulation optimization based on CPU time minimization.…
Implicit-explicit methods for a class of nonlinear nonlocal gradient flow equations modelling collective behaviour
2019
Abstract The numerical solution of nonlinear convection-diffusion equations with nonlocal flux by explicit finite difference methods is costly due to the local spatial convolution within the convective numerical flux and the disadvantageous Courant-Friedrichs-Lewy (CFL) condition caused by the diffusion term. More efficient numerical methods are obtained by applying second-order implicit-explicit (IMEX) Runge-Kutta time discretizations to an available explicit scheme for such models in Carrillo et al. (2015) [13] . The resulting IMEX-RK methods require solving nonlinear algebraic systems in every time step. It is proven, for a general number of space dimensions, that this method is well def…
Rational computing of energy levels for organic electronics: the case of 2-benzylidene-1,3-indandiones
2016
Device engineering in organic electronics, an active area of research, requires knowledge of the energy levels of organic materials (traditionally but ambiguously denoted as HOMO and LUMO). These can be effectively determined by electrochemical investigation, but yet more effective would be quantum chemical (QC) computation of these quantities. However, there is no consensus on the computational method in the research community. Ongoing discussions often focus on choosing the right density functional method, but neglect other model parameters, in particular, the basis set. This study considers comparison of various methodologies and parameters for predicting ionization energy I and electron…
Solution of self-consistent equations for the N3LO nuclear energy density functional in spherical symmetry. The program hosphe (v1.02)
2010
Abstract We present solution of self-consistent equations for the N 3 LO nuclear energy density functional. We derive general expressions for the mean fields expressed as differential operators depending on densities and for the densities expressed in terms of derivatives of wave functions. These expressions are then specified to the case of spherical symmetry. We also present the computer program hosphe (v1.02), which solves the self-consistent equations by using the expansion of single-particle wave functions on the spherical harmonic oscillator basis. Program summary Program title: HOSPHE (v1.02) Catalogue identifier: AEGK_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGK_…