Parallelization of an object-oriented FEM dynamics code: influence of the strategies on the Speedup

This paper presents an implementation in C++ of an explicit parallel finite element code dedicated to the simulation of impacts. We first present a brief overview of the kinematics and the explicit integration scheme with details concerning some particular points. Then we present the OpenMP parallelization toolkit used in order to parallelize our FEM code, and we focus on how the parallelization of the DynELA FEM code has been conducted for a shared memory system using OpenMP. Some examples are then presented to demonstrate the efficiency and accuracy of the proposed implementations concerning the Speedup of the code. Finally, an impact simulation application is presented and results are compared with the ones obtained by the commercial Abaqus explicit FEM code

A metamodel based optimisation algorithm for metal forming processes

Cost saving and product improvement have always been important goals in the metal\ud forming industry. To achieve these goals, metal forming processes need to be optimised. During\ud the last decades, simulation software based on the Finite Element Method (FEM) has significantly\ud contributed to designing feasible processes more easily. More recently, the possibility of\ud coupling FEM to mathematical optimisation algorithms is offering a very promising opportunity\ud to design optimal metal forming processes instead of only feasible ones. However, which\ud optimisation algorithm to use is still not clear.\ud In this paper, an optimisation algorithm based on metamodelling techniques is proposed\ud for optimising metal forming processes. The algorithm incorporates nonlinear FEM simulations\ud which can be very time consuming to execute. As an illustration of its capabilities, the\ud proposed algorithm is applied to optimise the internal pressure and axial feeding load paths\ud of a hydroforming process. The product formed by the optimised process outperforms products\ud produced by other, arbitrarily selected load paths. These results indicate the high potential of\ud the proposed algorithm for optimising metal forming processes using time consuming FEM\ud simulations

Solving optimisation problems in metal forming using Finite Element simulation and metamodelling techniques

During the last decades, Finite Element (FEM) simulations\ud of metal forming processes have become important\ud tools for designing feasible production processes. In more\ud recent years, several authors recognised the potential of\ud coupling FEM simulations to mathematical optimisation\ud algorithms to design optimal metal forming processes instead\ud of only feasible ones.\ud Within the current project, an optimisation strategy is being\ud developed, which is capable of optimising metal forming\ud processes in general using time consuming nonlinear\ud FEM simulations. The expression “optimisation strategy”\ud is used to emphasise that the focus is not solely on solving\ud optimisation problems by an optimisation algorithm, but\ud the way these optimisation problems in metal forming are\ud modelled is also investigated. This modelling comprises\ud the quantification of objective functions and constraints\ud and the selection of design variables.\ud This paper, however, is concerned with the choice for\ud and the implementation of an optimisation algorithm for\ud solving optimisation problems in metal forming. Several\ud groups of optimisation algorithms can be encountered in\ud metal forming literature: classical iterative, genetic and\ud approximate optimisation algorithms are already applied\ud in the field. We propose a metamodel based optimisation\ud algorithm belonging to the latter group, since approximate\ud algorithms are relatively efficient in case of time consuming\ud function evaluations such as the nonlinear FEM calculations\ud we are considering. Additionally, approximate optimisation\ud algorithms strive for a global optimum and do\ud not need sensitivities, which are quite difficult to obtain\ud for FEM simulations. A final advantage of approximate\ud optimisation algorithms is the process knowledge, which\ud can be gained by visualising metamodels.\ud In this paper, we propose a sequential approximate optimisation\ud algorithm, which incorporates both Response\ud Surface Methodology (RSM) and Design and Analysis\ud of Computer Experiments (DACE) metamodelling techniques.\ud RSM is based on fitting lower order polynomials\ud by least squares regression, whereas DACE uses Kriging\ud interpolation functions as metamodels. Most authors in\ud the field of metal forming use RSM, although this metamodelling\ud technique was originally developed for physical\ud experiments that are known to have a stochastic na-\ud ¤Faculty of Engineering Technology (Applied Mechanics group),\ud University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands,\ud email: [email protected]\ud ture due to measurement noise present. This measurement\ud noise is absent in case of deterministic computer experiments\ud such as FEM simulations. Hence, an interpolation\ud model fitted by DACE is thought to be more applicable in\ud combination with metal forming simulations. Nevertheless,\ud the proposed algorithm utilises both RSM and DACE\ud metamodelling techniques.\ud As a Design Of Experiments (DOE) strategy, a combination\ud of a maximin spacefilling Latin Hypercubes Design\ud and a full factorial design was implemented, which takes\ud into account explicit constraints. Additionally, the algorithm\ud incorporates cross validation as a metamodel validation\ud technique and uses a Sequential Quadratic Programming\ud algorithm for metamodel optimisation. To overcome\ud the problem of ending up in a local optimum, the\ud SQP algorithm is initialised from every DOE point, which\ud is very time efficient since evaluating the metamodels can\ud be done within a fraction of a second. The proposed algorithm\ud allows for sequential improvement of the metamodels\ud to obtain a more accurate optimum.\ud As an example case, the optimisation algorithm was applied\ud to obtain the optimised internal pressure and axial\ud feeding load paths to minimise wall thickness variations\ud in a simple hydroformed product. The results are satisfactory,\ud which shows the good applicability of metamodelling\ud techniques to optimise metal forming processes using\ud time consuming FEM simulations

High performance computing of explicit schemes for electrofusion jointing process based on message-passing paradigm

The research focused on heterogeneous cluster workstations comprising of a number of CPUs in single and shared architecture platform. The problem statements under consideration involved one dimensional parabolic equations. The thermal process of electrofusion jointing was also discussed. Numerical schemes of explicit type such as AGE, Brian, and Charlies Methods were employed. The parallelization of these methods were based on the domain decomposition technique. Some parallel performance measurement for these methods were also addressed. Temperature profile of the one dimensional radial model of the electrofusion process were also given

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Improvements to the APBS biomolecular solvation software suite

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining p$K_a$ values, and an improved web-based visualization tool for viewing electrostatics

Accelerating moderately stiff chemical kinetics in reactive-flow simulations using GPUs

The chemical kinetics ODEs arising from operator-split reactive-flow simulations were solved on GPUs using explicit integration algorithms. Nonstiff chemical kinetics of a hydrogen oxidation mechanism (9 species and 38 irreversible reactions) were computed using the explicit fifth-order Runge-Kutta-Cash-Karp method, and the GPU-accelerated version performed faster than single- and six-core CPU versions by factors of 126 and 25, respectively, for 524,288 ODEs. Moderately stiff kinetics, represented with mechanisms for hydrogen/carbon-monoxide (13 species and 54 irreversible reactions) and methane (53 species and 634 irreversible reactions) oxidation, were computed using the stabilized explicit second-order Runge-Kutta-Chebyshev (RKC) algorithm. The GPU-based RKC implementation demonstrated an increase in performance of nearly 59 and 10 times, for problem sizes consisting of 262,144 ODEs and larger, than the single- and six-core CPU-based RKC algorithms using the hydrogen/carbon-monoxide mechanism. With the methane mechanism, RKC-GPU performed more than 65 and 11 times faster, for problem sizes consisting of 131,072 ODEs and larger, than the single- and six-core RKC-CPU versions, and up to 57 times faster than the six-core CPU-based implicit VODE algorithm on 65,536 ODEs. In the presence of more severe stiffness, such as ethylene oxidation (111 species and 1566 irreversible reactions), RKC-GPU performed more than 17 times faster than RKC-CPU on six cores for 32,768 ODEs and larger, and at best 4.5 times faster than VODE on six CPU cores for 65,536 ODEs. With a larger time step size, RKC-GPU performed at best 2.5 times slower than six-core VODE for 8192 ODEs and larger. Therefore, the need for developing new strategies for integrating stiff chemistry on GPUs was discussed.Comment: 27 pages, LaTeX; corrected typos in Appendix equations A.10 and A.1