An application of quasi-Newton methods for the numerical solution of interface problems

Quasi-Newton methods are applied to solve interface problems which arise from domain decomposition methods. These interface problems are usually sparse systems of linear or nonlinear equations. We are interested in applying these methods to systems of linear equations where we are not able or willing to calculate the Jacobian matrices as well as to systems of nonlinear equations resulting from nonlinear elliptic problems in the context of domain decomposition. Suitability for parallel implementation of these algorithms on coarse-grained parallel computers is discussed.

Neutron quasi-elastic scattering in disordered solids: a Monte Carlo study of metal-hydrogen systems

The dynamic structure factor of neutron quasi-elastic scattering has been calculated by Monte Carlo methods for atoms diffusing on a disordered lattice. The disorder includes not only variation in the distances between neighbouring atomic sites but also variation in the hopping rate associated with each site. The presence of the disorder, particularly the hopping rate disorder, causes changes in the time-dependent intermediate scattering function which translate into a significant increase in the intensity in the wings of the quasi-elastic spectrum as compared with the Lorentzian form. The effect is particularly marked at high values of the momentum transfer and at site occupancies of the order of unity. The MC calculations demonstrate how the degree of disorder may be derived from experimental measurements of the quasi-elastic scattering. The model structure factors are compared with the experimental quasi-elastic spectrum of an amorphous metal-hydrogen alloy.

A multilevel algorithm for force-directed graph drawing

We describe a heuristic method for drawing graphs which uses a multilevel technique combined with a force-directed placement algorithm. The multilevel process groups vertices to form clusters, uses the clusters to define a new graph and is repeated until the graph size falls below some threshold. The coarsest graph is then given an initial layout and the layout is successively refined on all the graphs starting with the coarsest and ending with the original. In this way the multilevel algorithm both accelerates and gives a more global quality to the force- directed placement. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on a number of examples ranging from 500 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 30 seconds for a 10,000 vertex graph to around 10 minutes for the largest graph. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Components of error of maps from remotely sensed images

The concept of a “true” ground-truth map is introduced, from which the inaccuracy/error of any production map may be measured. A partition of the mapped region is defined in terms of the “residual rectification” transformation. Geometric RMS-type and Geometric Distortion error criteria are defined as well as a map mis-classification error criterion (the latter for hard and fuzzy produc-tion maps). The total map error is defined to be the sum (over each set of the map partition men-tioned above) of these three error components integrated over each set of the partition.

A multilevel algorithm for force-directed graph-drawing

We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a force-directed placement algorithm. The multilevel technique matches and coalesces pairs of adjacent vertices to define a new graph and is repeated recursively to create a hierarchy of increasingly coarse graphs, G0, G1, …, GL. The coarsest graph, GL, is then given an initial layout and the layout is refined and extended to all the graphs starting with the coarsest and ending with the original. At each successive change of level, l, the initial layout for Gl is taken from its coarser and smaller child graph, Gl+1, and refined using force-directed placement. In this way the multilevel framework both accelerates and appears to give a more global quality to the drawing. The algorithm can compute both 2 & 3 dimensional layouts and we demonstrate it on examples ranging in size from 10 to 225,000 vertices. It is also very fast and can compute a 2D layout of a sparse graph in around 12 seconds for a 10,000 vertex graph to around 5-7 minutes for the largest graphs. This is an order of magnitude faster than recent implementations of force-directed placement algorithms.

Collaborating components in mesh-based electronic packaging

From the model geometry creation to the model analysis, the stages in between such as mesh generation are the most manpower intensive phase in a mesh-based computational mechanics simulation process. On the other hand the model analysis is the most computing intensive phase. Advanced computational hardware and software have significantly reduced the computing time - and more importantly the trend is downward. With the kind of models envisaged coming, which are larger, more complex in geometry and modelling, and multiphysics, there is no clear trend that the manpower intensive phase is to decrease significantly in time - in the present way of operation it is more likely to increase with model complexity. In this paper we address this dilemma in collaborating components for models in electronic packaging application.

Computational modeling techniques for reliability of electronic components on printed circuit boards

This paper describes modeling technology and its use in providing data governing the assembly and subsequent reliability of electronic chip components on printed circuit boards (PCBs). Products, such as mobile phones, camcorders, intelligent displays, etc., are changing at a tremendous rate where newer technologies are being applied to satisfy the demands for smaller products with increased functionality. At ever decreasing dimensions, and increasing number of input/output connections, the design of these components, in terms of dimensions and materials used, is playing a key role in determining the reliability of the final assembly. Multiphysics modeling techniques are being adopted to predict a range of interacting physics-based phenomena associated with the manufacturing process. For example, heat transfer, solidification, marangoni fluid flow, void movement, and thermal-stress. The modeling techniques used are based on finite volume methods that are conservative and take advantage of being able to represent the physical domain using an unstructured mesh. These techniques are also used to provide data on thermal induced fatigue which is then mapped into product lifetime predictions.

Low Reynolds number turbulence models for accurate thermal simulations of electronic components

The electronics industry and the problems associated with the cooling of microelectronic equipment are developing rapidly. Thermal engineers now find it necessary to consider the complex area of equipment cooling at some level. This continually growing industry also faces heightened pressure from consumers to provide electronic product miniaturization, which in itself increases the demand for accurate thermal management predictions to assure product reliability. Computational fluid dynamics (CFD) is considered a powerful and almost essential tool for the design, development and optimization of engineering applications. CFD is now widely used within the electronics packaging design community to thermally characterize the performance of both the electronic component and system environment. This paper discusses CFD results for a large variety of investigated turbulence models. Comparison against experimental data illustrates the predictive accuracy of currently used models and highlights the growing demand for greater mathematical modelling accuracy with regards to thermal characterization. Also a newly formulated low Reynolds number (i.e. transitional) turbulence model is proposed with emphasis on hybrid techniques.

Turbulence modelling and its impact on CFD predictions for cooling of electronic components

This paper will discuss Computational Fluid Dynamics (CFD) results from an investigation into the accuracy of several turbulence models to predict air cooling for electronic packages and systems. Also new transitional turbulence models will be proposed with emphasis on hybrid techniques that use the k-ε model at an appropriate distance away from the wall and suitable models, with wall functions, near wall regions. A major proportion of heat emitted from electronic packages can be extracted by air cooling. This flow of air throughout an electronic system and the heat extracted is highly dependent on the nature of turbulence present in the flow. The use of CFD for such investigations is fast becoming a powerful and almost essential tool for the design, development and optimization of engineering applications. However turbulence models remain a key issue when tackling such flow phenomena. The reliability of CFD analysis depends heavily on the turbulence model employed together with the wall functions implemented. In order to resolve the abrupt fluctuations experienced by the turbulent energy and other parameters located at near wall regions and shear layers a particularly fine computational mesh is necessary which inevitably increases the computer storage and run-time requirements. The PHYSICA Finite Volume code was used for this investigation. With the exception of the k-ε and k-ω models which are available as standard within PHYSICA, all other turbulence models mentioned were implemented via the source code by the authors. The LVEL, LVEL CAP, Wolfshtein, k-ε, k-ω, SST and kε/kl models are described and compared with experimental data.

Lifetime assessment of electronic components for high reliability aerospace applications

This paper details a modelling approach for assessing the in-service (field) reliability and thermal fatigue life-time of electronic package interconnects for components used in the assembly of an aerospace system. The Finite Element slice model of a Plastic Ball Grid Array (PBGA) package and suitable energy based damage models for crack length predictions are used in this study. Thermal fatigue damage induced in tin-lead solder joints are investigated by simulating the crack growth process under a set of prescribed field temperature profiles that cover the period of operational life. The overall crack length in the solder joint for all different thermal profiles and number of cycles for each profile is predicted using a superposition technique. The effect of using an underfill is also presented. A procedure for verifying the field lifetime predictions for the electronic package by using reliability assessment under Accelerated Thermal Cycle (ATC) testing is also briefly outlined.

Modelling the reliability of components on flexible substrates

The use of flexible substrates is growing in many applications such as computer peripherals, hand held devices, telecommunications, automotive, aerospace, etc. The drive to adopt flexible circuits is due to their ability to reduce size, weight, assembly time and cost of final product. they also accommodate flexibility by allowing relative movement between component parts and provide a route for three dimensional packaging. This paper will describe some of the current research results from the Flex-No-Lead project, European Commission sponsored programme. The principle aim of this project is to investigate the processing, performance and reliability of flexible substrates when subjected to new environmentally friendly, lead-free soldering technologies. This paper will discuss the impact of specific design variables on performance and reliability. In particular the paper will focus on copper track designs, substrate material, dielectric material and solder mask defined joints

Multi-physics modelling for the fabrication, packaging and reliability of micro-systems components

The latest advances in multi-physics modelling both using high fidelity techniques and reduced order and behavioural models will be discussed. Particular focus will be given to the application and validation of these techniques for modelling the fabrication, packaging and subsequent reliability of micro-systems based components. The paper will discuss results from a number of research projects with particular emphasis on the techniques being developed in a major UK Goverment funded project - 3D-MINTEGRATION (www.3d-mintegration.com).

Predictive reliability and prognostics for electronic components: current capabilities and future challenges

Future analysis tools that predict the behavior of electronic components, both during qualification testing and in-service lifetime assessment, will be very important in predicting product reliability and identifying when to undertake maintenance. This paper will discuss some of these techniques and illustrate these with examples. The paper will also discuss future challenges for these techniques.