Hristos T. Anastassiu has been mainly involved in mathematical (analytical and numerical) methods, applied to electromagnetic problems, but he is also interested in laboratory applications. His research intererests include:
- Electromagnetic scattering theory and numerical computation of the Radar Cross Section (RCS) of realistic targets, focusing on inlets/cavities and dielectrically coated conductors. Also, scattering from rough surfaces (sea, buildings) applied to mobile communications.
- Mathematical modeling of electromagnetic diffraction, and the application of related methods to complex geometries.
- Pilot applications of relatively unknown mathematical techniques (e.g. bicomplex analysis) in electromagnetic problems.
- Development of novel algorithms in numerical analysis, aiming at the reduction of the computational cost in the solution of electromagnetic problems.
- Antenna theory and design, (patch antennas, loops, carbon nano tube antennas, smart antenna systems, e.t.c.).
- Wave propagation in free space and in waveguides, especially in curved geometries.
- Microwave links.
- Electromagnetic compatibility
- Non-cooperative target identification using RADAR data
- Fiber optics
The mathematical techniques he has invoked in his work include:
- Boundary value problems
- Integral equation techniques (e.g. the Wiener Hopf method)
- Complex analysis and asymptotics
- High frequency methods (Geometrical Optics - GO and Physical Optics - PO)
- Numerical techniques, such as Finite Element Method (FEM), Finite Difference Time Domain (FDTD), Adaptive Integral Method (AIM), Moment Method (MoM),
Method of Auxiliary Sources (MAS) e.t.c.
- Geometrical Theory of Diffraction (GTD), Uniform Theory of Diffraction (UTD), Physical Theory of Diffraction (PTD)
- Theory of waveguide discontinuities, such as Mode Matching (MM)
- Bicomplex analysis
As an undergraduate student at the Aristotle University of Thessaloniki he completed a Diploma thesis on wave propagation along curved dielectric waveguides. He invoked bicomplex analysis to solve this problem.
As a graduate student at the Ohio State University his M.Sc. thesis was focused on the analytic characterization of the electromagnetic scattering of a Gaussian beam from parabolic surfaces in two and three dimensions. His analysis was based mainly on Physical Optics (PO).
As a graduate student at the Department of Electrical Engineering of the University of Michigan he examined electromagnetic scattering from jet engine inlets, utilizing analytical (MM) and numerical (AIM) techniques. Along with his electromagnetic courses, he attended a large number of mandatory communication courses, focused on Noise Theory and Random Variables.
As a graduate student at the Department of Mathematics of the University of Michigan, his studies were focused on Applied Mathematics (Numerical Analysis, Complex Analysis, Boundary Value Problems e.t.c.).
As a Research Scientist at ICCS/NTUA he was involved in the following research projects, resulting in numerous scientific publications:
- Εlectromagnetic compatibility in airport environments, within the frame of the SIRENA research project (see “Participation in Research Projects”).
- Analysis and design of cylindrically conformal patch antenna arrays for aircraft and satellite communications within the frame of the MADS research project (see “Participation in Research Projects”). For the needs of this study he developed, together with his colleagues, a novel numerical method for the solution of scattering and radiation problems (Modified Method of Auxiliary Sources - MMAS).
- Convergence acceleration of the double series expressing the dyadic Green’s function within a waveguide with circular cross section.
- Application of the Method of Auxiliary Sources (MAS) to scattering from jet engine inlets.
- Combination of the Method of Auxiliary Sources (MAS) with the Standard Impedance Boundary Condition (SIBC) in problems involving scattering from dielectrically coated metal surfaces.
- Assessment of the advantages and disadvantages of the Method of Auxiliary Sources in comparison with standard methods, with emphasis to the computational complexity and the optimization of its characteristic parameters.
- Radar Cross Section (RCS) computation of various real life targets (e.g. aircraft, ships) in two and three dimensions.
- Development of Bicomplex (Quaternionic) Analysis and application to wave propagation. This topic is characterized by originality, it has already yielded a few significant results, and is expected to become useful for a wide range of problems in wave propagation within inhomogeneous media.
- Analysis and design of Ultra Wide Band (UWB) antennas for fast, short range communications. UWB technology is expected to revolutionize wireless links, promising to greatly increase data flow rates. It is also applicable to imaging behind obstacles, e.g. internal organs, unexploded ordnance including mines, archaeological artifacts e.t.c.
As a Research Scientist at HAI, he was involved in
- Εlectromagnetic compatibility issues, related to communication systems of the Hellenic Army, and especially to the “Hermes” system. He has conducted pertinent measurements at EMC Hellas (affiliated with HAI), and has cooperated with the British company DRS, both in Greece and in the UK.
- Εlectromagnetic compatibility in aircraft environment, within the frame of the HIRF SE research project (see “Participation in Research Projects”).
- Protection of aircraft against MANPADS, within the frame of the CASAM research project (see “Participation in Research Projects”).
- Circular loop arrays of large dimensions, for the analysis of which he developed a novel mathematical technique, yielding its characteristic parameters with high efficiency.
- Carbon Nanotube antennas. This area is completely novel, and the objective of the project is electromagnetic transmission and receipt of electromagnetic waves directly form the wing or fuselage, which has been reinforced with Carbon Nanotubes for aerodynamic reasons.
As an Adjunct Assistant Professor at the Hellenic Air Force Academy, he has supervised diploma theses, focusing on circular loop antenna arrays, Carbon Nanotube antennas, and has set the basics for a novel mathematical technique, called Circulant Adaptive Integral Method (see “Supervision of Diploma Theses”).
As a Professor at the TEI of Central Mecedonia he has been involved in research pertaining to electromagnetic propagation through orchards and in the analysis of microwave devices