Isogeometric analysis for elliptical waveguide eigenvalue problems

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 Helmholtz equation is weakened to a set of general eigenvalue equation by virtual work principal with discretized 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.