Complex structures and multiple interfaces of modern microelectronic packages complicate the interpretation of acoustic data. This study has four novel contributions. 1) Contributions to the finite element method. 2) Novel approaches to reduce computational cost. 3) New post processing technologies to interpret the simulation data. 4) Formation of theoretical guidance for acoustic image interpretation. The impact of simulation resolution on the numerical dispersion error and the exploration of quadrilateral infinite boundaries make up the first part of this thesis's contributions. The former focuses on establishing the convergence score of varying resolution densities in the time and spatial domain against a very high fidelity numerical solution. The latter evaluates the configuration of quadrilateral infinite boundaries in comparison against traditional circular infinite boundaries and quadrilateral Perfectly Matched Layers. The second part of this study features the modelling of a flip chip with a 140µm solder bump assembly, which is implemented with a 230MHz virtual raster scanning transducer with a spot size of 17µm. The Virtual Transducer was designed to reduce the total numerical elements from hundreds of millions to hundreds of thousands. Thirdly, two techniques are invented to analyze and evaluate simulated acoustic data: 1) The C-Line plot is a 2D max plot of specific gate interfaces that allows quantitative characterization of acoustic phenomena. 2) The Acoustic Propagation Map, contour maps an overall summary of intra sample wave propagation across the time domain in one image. Lastly, combining all the developments. The physical mechanics of edge effects was studied and verified against experimental data. A direct relationship between transducer spot size and edge effect severity was established. At regions with edge effect, the acoustic pulse interfacing with the solder bump edge is scattered mainly along the horizontal axis. The edge effect did not manifest in solder bump models without Under Bump Metallization (UBM). Measurements found acoustic penetration improvements of up to 44% with the removal of (UBM). Other acoustic mechanisms were also discovered and explored. Defect detection mechanism was investigated by modelling crack propagation in the solder bump assembly. Gradual progression of the crack was found have a predictable influence on the edge effect profile. By exploiting this feature, the progress of crack propagation from experimental data can be interpreted by evaluating the C-Scan image.

Over the last decades, there has been considerable attention in the accurate mathematical modeling and numerical simulations of free surface wave propagation in near-shore environments. A physical correct description of the large scale phenomena, which take place in the shallow water region, must account for strong nonlinear and dispersive effects, along with the interaction with complex topographies. First, a study on the behavior in nonlinear regime of different Boussinesq-type models is proposed, showing the advantage of using fully-nonlinear models with respect to weakly-nonlinear and weakly dispersive models (commonly employed). Secondly, a new flexible strategy for solving the fully-nonlinear and weakly-dispersive Green-Naghdi equations is presented, which allows to enhance an existing shallow water code by simply adding an algebraic term to the momentum balance and is particularly adapted for the use of hybrid techniques for wave breaking. Moreover, the first discretization of the Green-Naghdi equations on unstructured meshes is proposed via hybrid finite volume/ finite element schemes. Finally, the models and the methods developed in the thesis are deployed to study the physical problem of bore formation in convergent alluvial estuary, providing the first characterization of natural estuaries in terms of bore inception. / Ces dernières décennies, une attention particulière a été portée sur la modélisation mathématique et la simulation numérique de la propagation de vagues en environnements côtiers. Une description physiquement correcte des phénomènes à grande échelle, qui apparaissent dans les régions d'eau peu profonde, doit prendre en compte de forts effets non-linéaires et dispersifs, ainsi que l'interaction avec des bathymétries complexes. Dans un premier temps, une étude du comportement en régime non linéaire de différents modèles de type Boussinesq est proposée, démontrant l'avantage d'utiliser des modèles fortement non-linéaires par rapport à des modèles faiblement non-linéaires et faiblement dispersifs (couramment utilisés). Ensuite, une nouvelle approche flexible pour résoudre les équations fortement non-linéaires et faiblement dispersives de Green-Naghdi est présentée. Cette stratégie permet d'améliorer un code "shallow water" existant par le simple ajout d'un terme algébrique dans l'équation du moment et est particulièrement adapté à l'utilisation de techniques hybrides pour le déferlement des vagues. De plus, la première discrétisation des équations de Green-Naghdi sur maillage non structuré est proposée via des schémas hybrides Volume Fini/Élément Fini. Finalement, les modèles et méthodes développés dans la thèse sont appliqués à l'étude du problème physique de la formation du mascaret dans des estuaires convergents et alluviaux. Cela a amené à la première caractérisation d'estuaire naturel en terme d'apparition de mascaret.