Plane wave enriched Partition of Unity Isogeometric Analysis (PUIGA) for 2D-Helmholtz problems

Abstract

In general, numerical concerns in simulation of time harmonic acoustic waves are mainly due to the dispersion errors and the demands in modeling the problems with higher number of degrees of freedom per wavelength to obtain acceptable results. As a remedy, plane wave enriched Partition of Unity Finite Element Method (PUFEM) was earlier proposed by Melenk and Babuška (1996). Even though, PUFEM gives accurate results with lesser degrees of freedom and shows exponential convergence, it suffers from the approximate representation of geometry and leads to the boundary representation induced errors. In this regard, plane wave enriched PUFEM under Isogeometric framework named Partition of Unity Isogeometric Analysis (PUIGA) is proposed for accurate geometry representation and smooth solution approximation which can lead to a better solution. Several benchmark problems are considered in the present study, to illustrate the computational effectiveness of PUIGA.