Numerical optimisation of water curtain barriers design

The interactions between water curtain protective barriers and impinging cold gas clouds released during industrial accidents are simulated by a 2D finite difference code using a PSI-cell of the heat, mass and momentum transfer processes between the phases. A consistent derivation of the continuous phase source terms is presented. The results of early simulations of an existing 1:10 experimental model of a water curtain impacted by a cold gas cloud are presented for two typical curtain configurations.

Multilevel mesh partitioning for optimising aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut-edge weight, however it has been shown that for certain classes of solution algorithm, the convergence of the solver is strongly influenced by the subdomain aspect ratio. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Parallel optimisation algorithms for multilevel mesh partitioning

Three parallel optimisation algorithms, for use in the context of multilevel graph partitioning of unstructured meshes, are described. The first, interface optimisation, reduces the computation to a set of independent optimisation problems in interface regions. The next, alternating optimisation, is a restriction of this technique in which mesh entities are only allowed to migrate between subdomains in one direction. The third treats the gain as a potential field and uses the concept of relative gain for selecting appropriate vertices to migrate. The results are compared and seen to produce very high global quality partitions, very rapidly. The results are also compared with another partitioning tool and shown to be of higher quality although taking longer to compute.

Preface [Special Issue: International Symposium on Combinatorial Optimisation (CO2000)]

Preface [Special Issue containing a selection of papers presented at the International Symposium on Combinatorial Optimisation (CO2000) held at the University of Greenwich, London, from 12-14 July 2000.

Multi-physics-multi-scale simulation and optimisation: the next generation

FEA and CFD analysis is becoming ever more complex with an emerging demand for simulation software technologies that can address ranges of problems that involve combinations of interactions amongst varying physical phenomena over a variety of time and length scales. Computation modelling of such problems requires software technologies that enable the representation of these complex suites of 'physical' interactions. This functionality requires the structuring of simulation modules for specific physical phemonmena so that the coupling can be effectiely represented. These 'multi-physics' and 'multi-scale' computations are very compute intensive and so the simulation software must operate effectively in parallel if it is to be used in this context. Of course the objective of 'multi-physics' and 'multi-scale' simulation is the optimal design of engineered systems so optimistation is an important feature of such classes of simulation. In this presentation, a multi-disciplinary approach to simulation based optimisation is described with some key examples of application to challenging engineering problems.

Optimisation modelling for flip-chip solder joint reliability

This paper details and demonstrates integrated optimisation-reliability modelling for predicting the performance of solder joints in electronic packaging. This integrated modelling approach is used to identify efficiently and quickly the most suitable design parameters for solder joint performance during thermal cycling and is demonstrated on flip-chip components using “no-flow” underfills. To implement “optimisation in reliability” approach, the finite element simulation tool – PHYSICA, is coupled with optimisation and statistical tools. This resulting framework is capable of performing design optimisation procedures in an entirely automated and systematic manner.

Response Surface Modeling and Optimisation for Reliable Electronic Products

The aim of integrating computational mechanics (FEA and CFD) and optimization tools is to speed up dramatically the design process in different application areas concerning reliability in electronic packaging. Design engineers in the electronics manufacturing sector may use these tools to predict key design parameters and configurations (i.e. material properties, product dimensions, design at PCB level. etc) that will guarantee the required product performance. In this paper a modeling strategy coupling computational mechanics techniques with numerical optimization is presented and demonstrated with two problems. The integrated modeling framework is obtained by coupling the multi-physics analysis tool PHYSICA - with the numerical optimization package - Visua/DOC into a fuJly automated design tool for applications in electronic packaging. Thermo-mechanical simulations of solder creep deformations are presented to predict flip-chip reliability and life-time under thermal cycling. Also a thermal management design based on multi-physics analysis with coupled thermal-flow-stress modeling is discussed. The Response Surface Modeling Approach in conjunction with Design of Experiments statistical tools is demonstrated and used subsequently by the numerical optimization techniques as a part of this modeling framework. Predictions for reliable electronic assemblies are achieved in an efficient and systematic manner.

Multilevel refinement for combinatorial optimisation problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.

A combined evolutionary search and multilevel optimisation approach to graph-partitioning

The graph-partitioning problem is to divide a graph into several pieces so that the number of vertices in each piece is the same within some defined tolerance and the number of cut edges is minimised. Important applications of the problem arise, for example, in parallel processing where data sets need to be distributed across the memory of a parallel machine. Very effective heuristic algorithms have been developed for this problem which run in real-time, but it is not known how good the partitions are since the problem is, in general, NP-complete. This paper reports an evolutionary search algorithm for finding benchmark partitions. A distinctive feature is the use of a multilevel heuristic algorithm to provide an effective crossover. The technique is tested on several example graphs and it is demonstrated that our method can achieve extremely high quality partitions significantly better than those found by the state-of-the-art graph-partitioning packages.

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.

Reliability based design optimisation for system-in-package

This paper discusses a reliability based optimisation modelling approach demonstrated for the design of a SiP structure integrated by stacking dies one upon the other. In this investigation the focus is on the strategy for handling the uncertainties in the package design inputs and their implementation into the design optimisation modelling framework. The analysis of fhermo-mechanical behaviour of the package is utilised to predict the fatigue life-time of the lead-free board level solder interconnects and warpage of the package under thermal cycling. The SiP characterisation is obtained through the exploitation of Reduced Order Models (ROM) constructed using high fidelity analysis and Design of Experiments (DoE) methods. The design task is to identify the optimal SiP design specification by varying several package input parameters so that a specified target reliability of the solder joints is achieved and in the same time design requirements and package performance criteria are met

Numerical simulation of microwave thawing using a coupled solver approach

Thawing of a frozen food product in a domestic microwave oven is numerically simulated using a coupled solver approach. The approach consists of a dedicated electromagnetic FDTD solver and a closely coupled UFVM multi-physics package. Two overlapping numerical meshes are defined; the food material and container were meshed for heat transfer and phase change solution, whilst the microwave oven cavity and waveguide were meshed for the microwave irradiation. The two solution domains were linked using a cross-mapping routine. This approach allowed the rotation of the food load to be captured. Power densities obtained on the structured FDTD mesh were interpolated onto the UFVM mesh for each timestep/turntable position. The UFVM solver utilised the power density data to advance the temperature and phase distribution solution. The temperature-dependant dielectric and thermo-physical properties of the food load were updated prior to revising the electromagnetic solution. Changes in thermal/electric properties associated with the phase transition were fully accounted for as well as heat losses from product to cavity. Two scenarios were investigated: a centric and eccentric placement on the turntable. Developing temperature fields predicted by the numerical solution are validated against experimentally obtained data. Presented results indicate the feasibility of fully coupled simulations of the microwave heating of a frozen product. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)