Isogeometric collocation discretizations for acoustic wave problems

The acoustic wave problem is here discretized by collocation isogeometric analysis (IGA) in space and Newmark schemes of first and second order in time. A numerical study in the plane on both Cartesian and NURBS domains investigates the convergence rate of the proposed collocation Newmark-IGA method and its dependence on the main isogeometric parameters, the mesh size h, the spline polynomial degree p, the spline regularity k, and on the time step size Δt. In addition, a Ricker wavelet propagation test is accurately reproduced. The stability thresholds in time of the proposed method depend linearly on h and inversely on p. Therefore, the proposed collocation Newmark-IGA method retains the good convergence and stability properties of standard Galerkin IGA and spectral element discretizations of acoustic problems, as well as the high computational efficiency of collocation methods due to matrix sparsity and fast function evaluation.