Model Order Reduction for Circuit Equations

An ongoing project at the Dept. of Computer Science and Electrical Engineering deals with numeric modeling of electromagnetic properties. The method that is used is entitled the partial element equivalent circuit (PEEC) method and was developed at IBM in the early 70s. In the method, a system of electrical equivalent circuits are created to model the original electromagnetic problem. To find the solution, a large number of circuit equations needs to be created and solved. Realistic problems, antenna and printed circuit board analysis for example, can contain millions of unknown voltages and currents making a direct solution impossible due to computational limitations. By using model order reduction (MOR) techniques, the electromagnetic properties of the original PEEC model can be approximated using a mathematical model of reduced complexity. MOR for PEECs is a continuous developing subject due to the increasing popularity of the method and the need to reduce problem sizes within electromagnetic modeling.

The thesis goals are (1) to make an in-depth study on MOR techniques suitable for reducing PEEC models, (2) to implement the MOR in current C++ code, and (3) test reduced model results against full model simulations. You need basic knowledge in C++, circuit theory, and electromagnetics.