Mykhaylo Andriychuk is a well-known specialist in the field of mathematical modeling and numerical optimization of the characteristics of radiating and waveguide systems, and materials with specific properties as well. He developed the theory of mathematical modeling of such systems and materials based on a general operator representation of direct problem solutions, the application of a unified variational approach to determine optimal parameters that ensure the fulfillment of specified requirements within the selected optimization criterion. On this basis, the obtained theoretical results were used in the engineering practice of analysis and synthesis of planar radiating and waveguide systems, and in the formation of materials with desired electrodynamic or acoustic characteristics as well.
The scientific and applied results obtained by M. I. Andriychuk have found practical application, in particular in the design of microwave antenna systems, acoustic antennas and antenna arrays, as well as in the development of materials with specified acoustic and electromagnetic properties.