Complex analysis and convex optimization for EM design
2014-01-01 -> 2019-12-31
This project is about developing mathematical tools to solve fundamental problems in electromagnetic (EM) design of structures such as antennas, filters, phasors, absorbers, and cables. We will mainly work within the fields of complex analysis in one and several variables and convex as well as non-convex optimization. In complex analysis, we focus on representation theorems for various combinations of linear, time translational invariant, causal, and passive systems to derive performance bounds for EM systems. Optimization is used to analyze performance bounds and for automated optimal design of EM structures.
It is very time consuming and labor intensive to master the art of designing EM structures with specific electromagnetic properties. The design process includes usually physical modeling, rule of thumbs, computer simulations, optimization, and experimental verification. In this project, we incorporate the mathematical tools in the design process of electromagnetic devices to automatically design optimal EM structures and devices.
The specific mathematical objectives of this proposal are to:
develop representation theorems for causal systems that can be efficiently used to determine physical bounds, determine constraints on multi-parameter systems using complex analysis in several variables together with optimization, characterize optimal and near optimal solutions in a computationally efficient way for large structures, utilize the optimal solution computed using convex optimization for automated design of EM structures.
|Swedish Foundation for Strategic Research (SSF), Applied Mathematics