New full-wave algorithms for model order reduction and electromagnet analysis of impedance and scattering

As technology advances and sophisticated electronic systems achieve ubiquity, the demand for thorough, efficient Electromagnetic (EM) analysis continues to rise. The prohibitive costs of constructing and maintaining measurement facilities and designing and building system prototypes has fueled even greater demand for Computational Electromagnetics (CEM). Today’s CEM solvers can generate models that accurately characterize the EM behavior of an arbitrary structure presented for analysis. Two important applications for CEM are Scattering analysis of targets excited by EM waves and impedance modelling for the interconnect between the electronic components in Systems on Package (SoP) and Systems on Board (SoB). Often, the goal of analysis is to characterize behavior relative to parameters of interest, and EM solvers can generate parameter-dependent models of the system. The complexity of structures has increased so much that solving the solver-generated models at numerous desired parameter-points is a daunting computational task. For example, using these models in a simulator would be infeasible. Instead, existing Model Order Reduction (MOR) algorithms can construct reduced order models (ROMs) that characterize the parameter-dependent behavior of the original system. These existing methods are effective when the system of equations is linearly or weakly nonlinearly dependent on the parameters. When analyzing structures that are large compared to wavelengths of interest, retardation generates an exponentially nonlinear dependence on frequency, and such a strong nonlinearity makes it impossible to use existing MOR methods. This dissertation describes a new algorithm, Segregation by Primary Phase factors, that extends existing projection-based MOR techniques to the case of “Electromagnetically Large” structures. Extensions of the SPPF method to problems with parameter-dependent excitation are considered, as well as how to combine SPPF with fast integral equation solvers. Thesis Supervisor: Jacob K. White Title: Associate Director, Research Laboratory for Electronics