Profile

Publication details for Professor Jon Trevelyan

Laghrouche, O., El-Kacimi, A. & Trevelyan, J. (2010). A comparison of NRBCs for PUFEM in 2D Helmholtz problems at high wave numbers. Journal of Computational and Applied Mathematics 234(6): 1670-1677.

• Publication type: Journal papers: academic
• ISSN/ISBN: 0377-0427
• DOI: doi:10.1016/j.cam.2009.08.012
• Keywords: Helmholtz equation, Finite elements, Plane wave basis, Non-reflecting boundary conditions, Wave scattering
• View online: Online version

Author(s) from Durham

• Professor Jon Trevelyan

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.