Application of projection methods for studying the waveguide and resonance structures with singularities

The waveguide and resonance structures with singularities are studied in the case when a waveguide has reentrant edges and a resonator contains a dielectric of axial-symmetric shape with a piecewise constant radius inside. Mathematical models of such systems are proposed. Projection methods of various modifications are used. Efficient numerical algorithms are implemented on the basis of the proposed models.