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This paper is connected with the necessity of problem modeling and optimizing complex electrodynamic objects. A hollow structure is considered as such object. Its shape and main dimensions are set. It is required to determine the value of the size of the selected element to ensure the maximum average values of the characteristics of the object under study. In the course of modeling the scattering of electromagnetic waves, the method of integral equations was used. The collocation method was used to solve integral equations. The algorithm for determining the dimensions of an element of a hollow structure was developed. The approximation of the dependence of the element size on the length of the entire object was carried out.

The paper considers the design and characteristics of trigger scintillation counters based on silicon photomultipliers and fast scintillators. The experience of designing such devices is described and the results of research on development indicators are presented.