New Frontiers in Computational Electromagnetics: Towards High-Accuracy Solutions and Reliable Microwave Imaging

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Fast wireless communications, reliable power transmission, and biomedical imaging are the important technologies which define the quality of life for millions of Canadians. Critical to the advancements of these technologies is the design of novel devices and systems which rely on the methods and tools of computational electromagnetics (CEM). Among such systems are the cell phones, digital circuit boards, GPS units, radars, and tomography systems - just to name a few. Despite various fundamental advances made in the recent past, currently available algorithms of CEM suffer from various fundamental shortcomings. These shortcomings handicap development of the new technologies costing the industries millions of dollars in losses from faulty designs and prolonged time to market. The most challenging of these are large computational complexity of the pertinent algorithms and their inadequate accuracy when applied to electromagnetic analysis of realistic models. The proposed research program focuses on development of novel algorithms and high-accuracy solution methods, which overcome the computational complexity barrier and enable robust electromagnetic analysis of complex large-scale structures. The key contributions of the program are in development of novel, more economical, and more robust integral equation formulations for CEM as well as the novel higher-order numerical schemes for their solution. The novel integral equations proposed in the program will allow to reduce in half the size of the computational models stemming from the discretization of the realistic models. The proposed higher-order solution methods will further reduce the computational complexity by taking advantage of their exponentially higher efficiency compared to the low-order methods traditionally used in the industry.