Forward and Inverse Problems of Electromagnetics: Novel Algorithms and Their Implementations

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Computational electromagnetics (CEM) is foundational discipline that combines electrical engineering, mathematics, and computer science. It enables construction of methods and computational tools for electromagnetic analysis of microelectronic circuits, novel materials, scattering and radiation systems, wireless links in both indoors and cell level communication systems and other applications. Such analysis is critical for creation of new products and services providing higher levels of connectivity, security, and healthcare. Proposed program addresses current challenges, develops new algorithms, and explores important relationships between the methods in the forward and inverse problems of CEM. Construction of novel fast algorithms that break exponential growth in required data with the size of problem in CEM (a.k.a. 'curse of dimensionality') is one theme of the program. Such algorithms will make possible to solve more sophisticated and larger-scale problems of electromagnetic analysis than was possible previously. Development of new integral equations of electromagnetics and numerical schemes for their solution that can address fundamental challenges such as low-frequency instability, the presence of spurious resonances, oversampling breakdown and others, which have been plaguing computational software based on the classical integral equations of electromagnetics. The proposed methods will significantly enhance existing academic and commercial computational software packages and lead to new generation of electromagnetic solvers with drastically increased robustness and capacity. Elimination of ill-posedness (non-uniqueness of solution) in the inverse problems of microwave tomography (MWT) is another theme of the research program. Such ill-posedness for decades has been preventing microwaves from being used as main stream imaging modality alongside X-rays, ultrasounds, and MRI. We will exploit recently emerging prototypes of biology inspired antenna systems which have been demonstrated to possess unprecedented directivity. These new imaging system promises to eliminate ill-posedness featured in existing systems that prevents them from achieving desirable resolution. Proposed new MWT approach promises to find broad applications in radiology, non-destructive material testing of mechanical systems, security screening, remote sensing, and other areas.