SCALED BOUNDARY ISOGEOMETRIC ANALYSIS AND ITS APPLICATION I:EIGENVALUE PROBLEM OF WAVEGUIDE

Scaled boundary isogeometric analysis (SBIGA) is approved and applied for waveguide eigenvalue problem. Based on scaled boundary isogeometric transformation, the governing partial differential equations (PDEs) for waveguide eigenvalue problem are semi-weakened to a set of 2nd order ordinary differential equations (ODEs) by weighted residual methods, and transformed to a set of 1st order ODEs about the dynamic stiffness matrix in wavenumber domain. Approximating the dynamic stiffness matrix in the continued fraction expression and introducing auxiliary variables, the ODEs are finally exported to algebraic general eigenvalue equations, and thus the cutoff wavenumber of waveguide is obtained. The main property of SBIGA is that the governing PDEs are isogeometricly discretized on domain boundary, which reduces the spatial dimension by one and analytical feature in the radial direction like traditional SBFEM, additionally, boundary is exactly discretized as its geometry design. The numerical examples, including rectangular and L-shaped waveguides, are presented and compared with analytic solution and other numerical methods. The results show that SBIGA yields high precision results with fewer amounts of DOFs than other methods do.