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Boundary infinite elements for the Helmholtz equation in exterior domains
Author(s) -
Harari Isaac,
Barbone Paul E.,
Slavutin Michael,
Shalom Rami
Publication year - 1998
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/(sici)1097-0207(19980330)41:6<1105::aid-nme327>3.0.co;2-0
Subject(s) - classification of discontinuities , helmholtz equation , discretization , mathematics , helmholtz free energy , boundary element method , finite element method , computation , mathematical analysis , domain (mathematical analysis) , element (criminal law) , method of fundamental solutions , boundary value problem , boundary knot method , algorithm , engineering , physics , structural engineering , quantum mechanics , political science , law
A novel approach to the development of infinite element formulations for exterior problems of time‐harmonic acoustics is presented. This approach is based on a functional which provides a general framework for domain‐based computation of exterior problems. Special cases include non‐reflecting boundary conditions (such as the DtN method). A prominent feature of this formulation is the lack of integration over the unbounded domain, simplifying the task of discretization. The original formulation is generalized to account for derivative discontinuities across infinite element boundaries, typical of standard infinite element approximations. Continuity between finite elements and infinite elements is enforced weakly, precluding compatibility requirements. Various infinite element approximations for two‐dimensional configurations with circular interfaces are presented. Implementation requirements are relatively simple. Numerical results demonstrate the good performance of this scheme. © 1998 John Wiley & Sons, Ltd.