Parallel solution of high-order numerical schemes for solving incompressible flows

A new parallel numerical scheme for solving incompressible steady-state flows is presented. The algorithm uses a finite-difference approach to solving the Navier-Stokes equations. The algorithms are scalable and expandable. They may be used with only two processors or with as many processors as are available. The code is general and expandable. Any size grid may be used. Four processors of the NASA LeRC Hypercluster were used to solve for steady-state flow in a driven square cavity. The Hypercluster was configured in a distributed-memory, hypercube-like architecture. By using a 50-by-50 finite-difference solution grid, an efficiency of 74 percent (a speedup of 2.96) was obtained

Status of research at the Institute for Computer Applications in Science and Engineering (ICASE)

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science is summarized

Iterative methods for elliptic finite element equations on general meshes

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included

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

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

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Parameter estimation problems for distributed systems using a multigrid method

The problem of estimating spatially varying coefficients of partial differential equations is considered from observation of the solution and of the right hand side of the equation. It is assumed that the observations are distributed in the domain and that enough observations are given. A method of discretization and an efficient multigrid method for solving the resulting discrete systems are described. Numerical results are presented for estimation of coefficients in an elliptic and a parabolic partial differential equation

Lie series for celestial mechanics, accelerators, satellite stabilization and optimization

Lie series applications to celestial mechanics, accelerators, satellite orbits, and optimizatio