A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers

Authors:
O. Laghrouche;A. El-Kacimi;J. Trevelyan
Affiliations:
School of the Built Environment, Heriot-Watt University, Edinburgh EH14 4AS, UK;School of the Built Environment, Heriot-Watt University, Edinburgh EH14 4AS, UK;School of Engineering, Durham University, Durham DH1 3LE, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 6
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Abstract

In this work, exact and approximate non-reflecting boundary conditions (NRBCs) are implemented with the Partition of Unity Finite Element Method (PUFEM) to solve short wave scattering problems governed by the Helmholtz equation in two dimensions. By short wave problems, we mean situations in which the wavelength is a small fraction of the characteristic dimension of the scatterer. Various NRBCs are implemented and a comparison of their performance is carried out based on the accuracy of the results, ease of implementation and computational cost. The aim is to accurately model such problems in a reduced computational domain around the scatterer with fewer elements and without refining the mesh at each wave number.