Isogeometric Collocation for Time-Harmonic Waves in Acoustic Problems

Abstract

Isogeometric Analysis introduced by Hughes et al.[1] has gained importance in the recent times due to its ability to capture accurate solutions and exact geometry representations. In the present study, IGA-Collocation is extended for oscillatory problems in acoustics. Numerical solutions of oscillatory problems often suffer from numerical dispersion errors, which demands use of minimum of ten nodes per wavelength or higher order bases. But employing higher order bases in IGA based on Galerkin approach (IGA-G) is computationally expensive. To overcome this issue, we employed IGA based on Collocation (IGA-C)[2] which is often regarded as a rank sufficient one-point quadrature scheme and has the potential to reduce the computational cost. In the present study, IGA-C with higher order bases is employed for solving rectangular waveguide and oscillating cylinder problems with different wave numbers. The performance of IGA-C is compared with the IGA-G in terms of efficacy and computational time. From the results, the potential of IGA-C is clearly observed in solving wave problems.