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.

Keywords: waveguide, resonator, reentrant edges, reentrant corners, projection methods

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