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Bubble‐based stabilization for the Helmholtz equation
Author(s) -
Harari Isaac,
Gosteev Kirill
Publication year - 2006
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.1930
Subject(s) - series (stratigraphy) , helmholtz equation , truncation (statistics) , bubble , representation (politics) , harmonic , mathematics , helmholtz free energy , dispersion (optics) , mathematical analysis , calculus (dental) , computer science , acoustics , physics , statistics , boundary value problem , optics , dentistry , quantum mechanics , politics , political science , law , biology , medicine , paleontology , parallel computing
A comparison of two bubble‐enriched methods, derived by different considerations, indicates that the methods are identical in some cases. Thus, series representations of auxiliary functions, derived independently for the two methods, turn out to be equivalent prior to truncation. Three such series for time‐harmonic acoustics are considered. Dispersion analysis points to the more efficient series representation and provides guidelines for the number of terms to be retained. Numerical tests confirm the validity of these practical guidelines. Copyright © 2006 John Wiley & Sons, Ltd.