Explicit second order isogeometric discretizations for acoustic wave problems

This paper presents a stability analysis of isogeometric (IGA) and explicit Newmark discretizations for acoustic wave problems with absorbing boundary conditions. In spite of the very ill-conditioned IGA mass and stiffness matrices, especially with respect to the polynomial degree p of the B-splines and Non-Uniform Rational B-Splines (NURBS) basis functions employed, the stability bounds of the proposed Newmark-IGA method depend linearly on the meshsize h of the IGA mesh and inversely on the IGA polynomial degree p. Several numerical tests in the plane confirm these stability bounds and additionally explore the Newmark-IGA order of convergence with respect to h,p,Δt, domain deformation and the absorbing boundary conditions performance in the presence of a Ricker wavelet in a NURBS domain