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CONSISTENT INFINITESIMAL FINITE‐ELEMENT CELL METHOD: THREE‐DIMENSIONAL VECTOR WAVE EQUATION
Author(s) -
SONG CHONGMIN,
WOLF J. P.
Publication year - 1996
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(19960715)39:13<2189::aid-nme950>3.0.co;2-p
Subject(s) - finite element method , mathematical analysis , mixed finite element method , infinitesimal , extended finite element method , mathematics , boundary knot method , discretization , geometry , smoothed finite element method , boundary element method , physics , thermodynamics
To calculate the unit‐impulse response matrix of an unbounded medium for use in a time‐domain analysis of unbounded medium–structure interaction, the consistent infinitesimal finite‐element cell method is developed for the three‐dimensional vector wave equation. This is a boundary finite‐element procedure. The discretization is only performed on the structure–medium interface, yielding a reduction of the spatial dimension by 1. The procedure is rigorous in the radial direction and exact in the finite‐element sense in the circumferential directions. In contrast to the boundary‐element procedure, the consistent infinitesimal finite‐element cell method does not require a fundamental solution and incorporates interfaces extending from the structure–medium interface to infinity compatible with similarity without any additional computational effort. A general anisotropic material can be processed. The derivation is based on the finite‐element formulation and on similarity.