The cutoff wavenumbers of elliptical waveguides were calculated by using isogeomtric analysis method （IGA）. With NURBS basis functions in IGA, the computational model was consistent with geometric model imported fro...The cutoff wavenumbers of elliptical waveguides were calculated by using isogeomtric analysis method （IGA）. With NURBS basis functions in IGA, the computational model was consistent with geometric model imported from CAD system. The field variable （longitudinal electric/magnetic field） was constructed by the same NURBS basis functions as the representation of geometric model. In the refinement procedure used to get a more accurate solution, communication with original CAD system is unnecessary and the geometric shape is kept unchanged. The Helrnholtz equation is weakened to a set of general eigenvalue equation by virtual work principal with diseretized degree-of-freedom on control points. Elliptical waveguides with three typical eccentricities, 0.1, 0.5 and 0.9, are calculated by IGA with different size mesh. The first four cutoff wavenumbers are obtained even in coarse mesh and the RMS of first 25 cutoff wavenumbers has much more swift convergence rate with decreasing the mesh size than traditional FEM. The accuracy and robustness of the proposed method are validated by elliptical waveguides, and also the method can be applied to waveguides with arbitrary cross sections.展开更多
Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic me...Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic media is derived; then the eigenequation for it is given. When an elliptical waveguide becomes a circular waveguide, the electromagnetic fields and the eigenequation of the circular waveguide can be obtained from the eigenequation of the elliptical waveguide using the asymptotic formulae of Mathieu and modified Mathieu functions for a large radial coordinate in the elliptical coordinate system, and the eigenequation of a circular waveguide filled with multilayered dielectrics can be treated as a special case of an elliptical waveguide. In addition, some numerical examples are presented to analyze the propagating characteristics influenced by the permittivity, permeability of dielectrics filled in the elliptical waveguide, etc. The results show that changing the permittivity or permeability of the dielectrics filled in the waveguide and the major semiaxis value of the i-th layer can change the propagating characteristics of an elliptical waveguide.展开更多
基金Project(GZ566) supported by the China-German Joint Research FoundationProjects(51138011, 51109134) supported by the National Natural Science Foundation of China
文摘The cutoff wavenumbers of elliptical waveguides were calculated by using isogeomtric analysis method （IGA）. With NURBS basis functions in IGA, the computational model was consistent with geometric model imported from CAD system. The field variable （longitudinal electric/magnetic field） was constructed by the same NURBS basis functions as the representation of geometric model. In the refinement procedure used to get a more accurate solution, communication with original CAD system is unnecessary and the geometric shape is kept unchanged. The Helrnholtz equation is weakened to a set of general eigenvalue equation by virtual work principal with diseretized degree-of-freedom on control points. Elliptical waveguides with three typical eccentricities, 0.1, 0.5 and 0.9, are calculated by IGA with different size mesh. The first four cutoff wavenumbers are obtained even in coarse mesh and the RMS of first 25 cutoff wavenumbers has much more swift convergence rate with decreasing the mesh size than traditional FEM. The accuracy and robustness of the proposed method are validated by elliptical waveguides, and also the method can be applied to waveguides with arbitrary cross sections.
文摘Using the method of separation of variables in the elliptical coordinate system, a recursive formula for the electromagnetic fields in a confocal elliptical waveguide filled with multi-layered homogeneous isotropic media is derived; then the eigenequation for it is given. When an elliptical waveguide becomes a circular waveguide, the electromagnetic fields and the eigenequation of the circular waveguide can be obtained from the eigenequation of the elliptical waveguide using the asymptotic formulae of Mathieu and modified Mathieu functions for a large radial coordinate in the elliptical coordinate system, and the eigenequation of a circular waveguide filled with multilayered dielectrics can be treated as a special case of an elliptical waveguide. In addition, some numerical examples are presented to analyze the propagating characteristics influenced by the permittivity, permeability of dielectrics filled in the elliptical waveguide, etc. The results show that changing the permittivity or permeability of the dielectrics filled in the waveguide and the major semiaxis value of the i-th layer can change the propagating characteristics of an elliptical waveguide.
