With the rapid increase in the speed and complexity of integrated circuit designs, 3D full wave and time domain simulation of chip, package, and board systems becomes more and more important for the engineering of modern designs. Much effort has been applied to the problem of electromagnetic (EM) simulation of such systems in recent years. Major advances in boundary element EM simulations have led to O(n log n) simulations using iterative methods and advanced Fast. Fourier Transform (FFT), Multi-Level Fast Multi-pole Methods (MLFMM), and low-rank matrix compression techniques. These advances have been augmented with an explosion of multi-core and distributed computing technologies, however, realization of the full scale of these capabilities has been hindered by cumbersome and inefficient geometric processing. Anecdotal evidence from industry suggests that users may spend around 80% of turn-around time manipulating the geometric model and mesh.;This dissertation addresses this problem by developing fast and efficient data structures and algorithms for 3D modeling of chips, packages, and boards. The methods proposed here harness the regular, layered 2D nature of the models (often referred to as "2.5D") to optimize these systems for large geometries. First, an architecture is developed for efficient storage and manipulation of 2.5D models. The architecture gives special attention to native representation of structures across various input models and special issues particular to 3D modeling.;The 2.5D structure is then used to optimize the mesh systems First, circuit/EM co-simulation techniques are extended to provide electrical connectivity between objects. This concept is used to connect independently meshed layers, allowing simple and efficient 2D mesh algorithms to be used in creating a 3D mesh. Here, adaptive meshing is used to ensure that the mesh accurately models the physical unknowns (current and charge).;Utilizing the regularized nature of 2.5D objects and the known characteristics of stripline, microstrip, and coplanar waveguide propagation, rules are developed to predictively mesh 2.5D models. Creating the meshes based on this a priori knowledge eliminates the expensive solver adaptation loop commonly used to model EM structures. In addition, this method allows for the use of long, thin triangles following the predominate current paths at high frequencies, greatly reducing the number of mesh elements required to model the interactions accurately.
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