Applications of finite element computer modelling and thermal infrared remote sensing to the study of geothermal anomalies

Buried heat sources can be investigated by examining thermal infrared images and comparing these with the results of theoretical models which predict the thermal anomaly a given heat source may generate. Key factors influencing surface temperature include the geometry and temperature of the heat source, the surface meteorological environment, and the thermal conductivity and anisotropy of the rock. In general, a geothermal heat flux of greater than 2% of solar insolation is required to produce a detectable thermal anomaly in a thermal infrared image. A heat source of, for example, 2-300K greater than the average surface temperature must be a t depth shallower than 50m for the detection of the anomaly in a thermal infrared image, for typical terrestrial conditions. Atmospheric factors are of critical importance. While the mean atmospheric temperature has little significance, the convection is a dominant factor, and can act to swamp the thermal signature entirely. Given a steady state heat source that produces a detectable thermal anomaly, it is possible to loosely constrain the physical properties of the heat source and surrounding rock, using the surface thermal anomaly as a basis. The success of this technique is highly dependent on the degree to which the physical properties of the host rock are known. Important parameters include the surface thermal properties and thermal conductivity of the rock. Modelling of transient thermal situations was carried out, to assess the effect of time dependant thermal fluxes. One-dimensional finite element models can be readily and accurately applied to the investigation of diurnal heat flow, as with thermal inertia models. Diurnal thermal models of environments on Earth, the Moon and Mars were carried out using finite elements and found to be consistent with published measurements. The heat flow from an injection of hot lava into a near surface lava tube was considered. While this approach was useful for study, and long term monitoring in inhospitable areas, it was found to have little hazard warning utility, as the time taken for the thermal energy to propagate to the surface in dry rock (several months) in very long. The resolution of the thermal infrared imaging system is an important factor. Presently available satellite based systems such as Landsat (resolution of 120m) are inadequate for detailed study of geothermal anomalies. Airborne systems, such as TIMS (variable resolution of 3-6m) are much more useful for discriminating small buried heat sources. Planned improvements in the resolution of satellite based systems will broaden the potential for application of the techniques developed in this thesis. It is important to note, however, that adequate spatial resolution is a necessary but not sufficient condition for successful application of these techniques.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Dynamic load-balancing of finite element applications with the DRAMA library

The DRAMA library, developed within the European Commission funded (ESPRIT) project DRAMA, supports dynamic load-balancing for parallel (message-passing) mesh-based applications. The target applications are those with dynamic and solution-adaptive features. The focus within the DRAMA project was on finite element simulation codes for structural mechanics. An introduction to the DRAMA library will illustrate that the very general cost model and the interface designed specifically for application requirements provide simplified and effective access to a range of parallel partitioners. The main body of the paper will demonstrate the ability to provide dynamic load-balancing for parallel FEM problems that include: adaptive meshing, re-meshing, the need for multi-phase partitioning.

Dynamic multi-partitioning for parallel finite element applications

The central product of the DRAMA (Dynamic Re-Allocation of Meshes for parallel Finite Element Applications) project is a library comprising a variety of tools for dynamic re-partitioning of unstructured Finite Element (FE) applications. The input to the DRAMA library is the computational mesh, and corresponding costs, partitioned into sub-domains. The core library functions then perform a parallel computation of a mesh re-allocation that will re-balance the costs based on the DRAMA cost model. We discuss the basic features of this cost model, which allows a general approach to load identification, modelling and imbalance minimisation. Results from crash simulations are presented which show the necessity for multi-phase/multi-constraint partitioning components

Experimental and modeling analysis of the reliability of the anisotropic conductive films

Experiments as well as computer modeling methods have been used to investigate the effect of the solder reflow process on the electrical characteristics and reliability of anisotropic conductive film (ACF) interconnections. In the experiments, the contact resistance of the ACF interconnections was found to increase after a subsequent reflow and the magnitude of this increase was strongly correlated to the peak temperature of the reflow profile. In fact, nearly 40 percent of the joints were opened (i.e. lifted away from the pad) after the reflow with a peak temperature of 260 OC while no openings was observed when the peak temperature was 210 "C. It is believed that the CTE mismatch between the polymer particle and the adhesive matrix is the main cause of this contact degradation. To understand this phenomenon better, a 3-D model of an ACF joint structure was built and Finite Element Analysis was used to predict the stress distrihution in the conductive particles, adhesive matrix and metal pads during the reflow process. The effects of the peak temperature, the CTE of the adhesive matrix and the bump height on the reliability of the ACF interconnections were discussed.

Computational methodology for analysis of historic composite structures

This paper details the computational methodology for analysis of the structural behaviour of historic composite structures. The modelling approach is based on finite element analysis and has been developed to aid the efficient and inexpensive computational mechanics of complex composite structures. The discussion is primarily focussed on the modelling methodology and analysis of structural designs that comprise of structural beam components acting as stiffeners to a wider shell part of the structure. A computational strategy for analysis of this type of composite structures that exploits their representation through smeared shell models is detailed in the paper.

Thermo-mechanical analysis of the packaging process for micro-electronic displays

Micro-electronic displays are sensitive devices and its performance is easily affected by external environmental factors. To enable the display to perform in extreme conditions, the device must be structurally strengthened, the effects of this packaging process was investigated. A thermo-mechanical finite element analysis was used to discover potential problems in the packaging process and to improve the overall design of the device. The main concern from the analysis predicted that displacement of the borosilicate glass and the Y stress of the adhesive are important. Using this information a design which reduced the variation of displacement and kept the stress to a minimum was suggested

Reliability analysis of SiP structures

This presentation discusses latest developments in SiP technology and the challenges for design in terms of manufacture and reliability. It presents results from a UK government funded project that aims to develop modelling techniques that will assess the thermo-mechanical reliability of SiP structures such as (i) stacked die, (ii) side-by-side dies and (iii) embedded die. Finite element analysis coupled with numerical optimisation and uncertainty analysis is used is used to model the reliability of a particular package design. In particular, the damage (energy density) in the lead free solder interconnects under accelerated temperature cycling is predicted and used to observe the fatigue life-time. Warpage of the structure is also investigated