Complex wavenumber Fourier analysis of the B-spline based finite element method

We present the results of one-dimensional complex wavenumber Fourier analysis of the B-spline variant of Finite Element Method (FEM). Generally, numerical results of elastic wave propagation in solids obtained by FEM are polluted by dispersion and attenuation. It was shown for the higher-order B-spline based FEM, that the optical modes did not occur in the case of infinite domains, unlike the higher-order Lagrangian and Hermitian finite elements, and also the dispersion errors are smaller. The paper’s main focus is on the wave propagation through B-spline multi-patch/segment discretization with the C⁰$C^0$ connection of B-spline segments and, chiefly, to the determining of dispersion and attenuation dependences. The numerical approach employed leads to substantial minimization of dispersion errors. Furthermore, the errors decrease in line with the increasing order of the B-spline elements/segments, with the local refinement, and also by the particular choice of the positions of control points through the optimizing procedure.