Multilevel refinement for the vehicle routing problem

Multilevel approaches to computational problems are pervasive across many areas of applied mathematics and scientific computing. The multilevel paradigm uses recursive coarsening to create a hierarchy of approximations to the original problem, then an initial solution is found for the coarsest problem and iteratively refined and improved at each level, coarsest to finest. The solution process is aided by the global perspective (or `global view') imparted to the optimisation by the coarsening. This paper looks at their application to the Vehicle Routing Problem.

[Book review] Mathematics and Culture II

Review of Mathematics and Culture II. Visual Perfection: Mathematics and Creativity, Michele Emmer (Ed.), Springer, 2005 ISBN: 978-3-540-21368-0

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

Use of a coupled mechanical-acoustic computational model to identify failure mechanisms in paper production

In this paper, a couple mechanical-acoustic system of equations is solved to determine the relationship between emitted sound and damage mechanisims in paper under controlled stress conditions. The simple classical expression describing the frequency of a plucked string to its material properties is used to generate a numberical representation of the microscopic structue of the paper, and the resulting numerical model is then used to simulate the vibration of a range of simple fibre structures when undergoing two distinct types of damange mechanisms: (a)fibre/fibre bond failure, (b) fibre failure. The numercial results are analysed to determine whether there is any detectable systematic difference between the resulting acoustic emissions of the two damage processes. Fourier techniques are then used to compare th computeed results against experimental measurements. Distinct frequency components identifying each type of damage are shown to exist, and in this respect theory and experiments show good correspondece. Hence, it is shown, that althrough the mathematical model represents a grossly-simplified view of the complex structure of the paper, it nevertheless provides a good understanding of the underlying micro-mechanisms characterising its proeperties as a stress-resisting structure. Use of the model and acoompanying software will enable operators to identify approaching failure conditions in the continuous production of paper from emitted sound signals and take preventative action.

CFD fire simulation of the Swissair flight 111 in-flight fire - part II: fire spread analysis

In 1998, Swissair Flight I I I (SR111) developed an in-flight fire shortly after take-off which resulted in the loss of the aircraft, a McDonnell Douglas MD-I 1, and all passengers and crew. The Transportation Safety Board (TSB) of Canada, Fire and Explosion Group launched a four year investigation into the incident in an attempt to understand the cause and subsequent mechanisms which lead to the rapid spread of the in-flight fire. As part of this investigation, the SMARTFIRE Computational Fluid Dynamics (CFD) software was used to predict the 'possible' development of the fire and associated smoke movement. In this paper the CFD fire simulations are presented and model predictions compared with key findings from the investigation. The model predictions are shown to be consistent with a number of the investigation findings associated with the early stages of the fire development. The analysis makes use of simulated pre-fire airflow conditions within the MD-11 cockpit and above ceiling region presented in an earlier publication (Part 1) which was published in The Aeronautical Journal in January 2006(4).

Application of simulation technologies in the analysis of granular material behaviour during transport and storage

Problems in the preservation of the quality of granular material products are complex and arise from a series of sources during transport and storage. In either designing a new plant or, more likely, analysing problems that give rise to product quality degradation in existing operations, practical measurement and simulation tools and technologies are required to support the process engineer. These technologies are required to help in both identifying the source of such problems and then designing them out. As part of a major research programme on quality in particulate manufacturing computational models have been developed for segregation in silos, degradation in pneumatic conveyors, and the development of caking during storage, which use where possible, micro-mechanical relationships to characterize the behaviour of granular materials. The objective of the work presented here is to demonstrate the use of these computational models of unit processes involved in the analysis of large-scale processes involving the handling of granular materials. This paper presents a set of simulations of a complete large-scale granular materials handling operation, involving the discharge of the materials from a silo, its transport through a dilute-phase pneumatic conveyor, and the material storage in a big bag under varying environmental temperature and humidity conditions. Conclusions are drawn on the capability of the computational models to represent key granular processes, including particle size segregation, degradation, and moisture migration caking.

Computational modelling of multi-physics and multi-scale processes in parallel

This paper provides an overview of the developing needs for simulation software technologies for the computational modelling of problems that involve combinations of interactions amongst varying physical phenomena over a variety of time and space scales. Computational modelling of such problems requires software tech1nologies that enable the mathematical description of the interacting physical phenomena together with the solution of the resulting suites of equations in a numerically consistent and compatible manner. This functionality requires the structuring of simulation modules for specific physical phenomena so that the coupling can be effectively represented. These multi-physics and multi-scale computations are very compute intensive and the simulation software must operate effectively in parallel if it is to be used in this context. An approach to these classes of multi-disciplinary simulation in parallel is described, with some key examples of application to2 challenging engineering problems.

Matching search in fractal video compression and its parallel implementation in distributed computing environments

Fractal video compression is a relatively new video compression method. Its attraction is due to the high compression ratio and the simple decompression algorithm. But its computational complexity is high and as a result parallel algorithms on high performance machines become one way out. In this study we partition the matching search, which occupies the majority of the work in a fractal video compression process, into small tasks and implement them in two distributed computing environments, one using DCOM and the other using .NET Remoting technology, based on a local area network consists of loosely coupled PCs. Experimental results show that the parallel algorithm is able to achieve a high speedup in these distributed environments.

On a parallel time-domain method for the nonlinear Black-Scholes equation

A parallel time-domain algorithm is described for the time-dependent nonlinear Black-Scholes equation, which may be used to build financial analysis tools to help traders making rapid and systematic evaluation of buy/sell contracts. The algorithm is particularly suitable for problems that do not require fine details at each intermediate time step, and hence the method applies well for the present problem.

Computational modelling for reliable flip-chip packaging at sub-100 micron pitch using isotropic conductive adhesives

This paper presents the assembly process using next generation electroformed stencils and Isotropic Conductive Adhesives (ICAs) as interconnection material. The utilisation of ICAs in flip-chip assembly process is investigated as an alternative to the lead and lead-free solder alloys and aims to ensure a low temperature (T < 100 °C) assembly process. The paper emphasizes and discusses in details the assembly of a flip-chip package based on copper columns bumped die and substrate with stencil printed ICA deposits at sub-100 μm pitch. A computational modelling approach is undertaken to provide comprehensive results on reliability trends of ICA joints subject to thermal cycling of the flip-chip assembly based on easy to use damage criteria and damage evaluation. Important design parameters in the package are selected and investigated using numerical modelling techniques to provide knowledge and understanding of their impact on the thermo-mechanical behaviour of the flip-chip ICA joints. Sensitivity analysis of the damage in the adhesive material is also carried out. Optimal design rules for enhanced performance and improved thermo-mechanical reliability of ICA assembled flip-chip packages are finally formulated.

Optimisation modelling for design of advanced interconnects

This paper describes a computational strategy for virtual design and prototyping of electronic components and assemblies. The design process is formulated as a design optimisation problem. The solution of this problem identifies not only the design which meets certain user specified requirements but also the design with the maximum possible improvement in particular aspects such as reliability, cost, etc. The modelling approach exploits numerical techniques for computational analysis (Finite Element Analysis) integrated with numerical methods for approximation, statistical analysis and optimisation. A software framework of modules that incorporates the required numerical techniques is developed and used to carry out the design optimisation modelling of fine-pitch flip-chip lead free solder interconnects.

A computational study of segregation in granular material during heaping

A continuum model of the flow of granular material during silo filling using a viscoplastic constitutive relation is presented in this paper. The constitutive model is based on the Drucker-Prager plasticity yield function. The simulation results give a realistic representation of complex features of granular flows during filling processes, such as heap formation and non-zero inclination angle of the material-air interface. The model is also coupled within the same framework with novel micro-mechanical parametrisations and the process of segregation during filling of granular mixtures can also be modelled.

Support vector machines for regression and applications to software quality prediction

Software metrics are the key tool in software quality management. In this paper, we propose to use support vector machines for regression applied to software metrics to predict software quality. In experiments we compare this method with other regression techniques such as Multivariate Linear Regression, Conjunctive Rule and Locally Weighted Regression. Results on benchmark dataset MIS, using mean absolute error, and correlation coefficient as regression performance measures, indicate that support vector machines regression is a promising technique for software quality prediction. In addition, our investigation of PCA based metrics extraction shows that using the first few Principal Components (PC) we can still get relatively good performance.

Semi-Lagrange time integration for PDE models of asian options

Semi-Lagrange time integration is used with the finite difference method to provide accurate stable prices for Asian options, with or without early exercise. These are combined with coordinate transformations for computational efficiency and compared with published results