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Improved accuracy for the Helmholtz equation in unbounded domains
Author(s) -
Turkel Eli,
Farhat Charbel,
Hetmaniuk Ulrich
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.882
Subject(s) - helmholtz equation , computation , wavenumber , forcing (mathematics) , mathematics , mathematical analysis , helmholtz free energy , function (biology) , boundary (topology) , variable (mathematics) , boundary value problem , scattering , mode (computer interface) , physics , algorithm , computer science , optics , quantum mechanics , evolutionary biology , biology , operating system
Based on properties of the Helmholtz equation, we derive a new equation for an auxiliary variable. This reduces much of the oscillations of the solution leading to more accurate numerical approximations to the original unknown. Computations confirm the improved accuracy of the new models in both two and three dimensions. This also improves the accuracy when one wants the solution at neighbouring wavenumbers by using an expansion in k . We examine the accuracy for both waveguide and scattering problems as a function of k , h and the forcing mode l . The use of local absorbing boundary conditions is also examined as well as the location of the outer surface as functions of k . Connections with parabolic approximations are analysed. Copyright © 2004 John Wiley & Sons, Ltd.