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High‐order absorbing boundary conditions incorporated in a spectral element formulation
Author(s) -
Kucherov Leonid,
Givoli Dan
Publication year - 2010
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1188
Subject(s) - spectral element method , finite element method , mathematics , convergence (economics) , boundary value problem , mathematical analysis , spectral method , boundary (topology) , order (exchange) , exponential function , domain (mathematical analysis) , polynomial , element (criminal law) , extended finite element method , physics , law , finance , economics , thermodynamics , economic growth , political science
The solution of the time‐dependent wave equation in a semi‐infinite wave guide is considered. An artificial boundary ℬ is introduced, which encloses a finite computational domain. On ℬ the Hagstrom–Warburton (H–W) local high‐order absorbing boundary condition (ABC) is imposed. In contrast to previous studies, which involved either finite difference schemes or low‐order finite element schemes, here the way to incorporate the H–W ABC into a spectral element formulation is shown. To this end, the Seriani–Priolo spectral element is used in space and a 4th‐order Runge–Kutta scheme is employed in time. This leads to exponential convergence in both the polynomial order of the spectral element, and in the order of the ABC, and thus avoids the convergence rate inconsistency which is otherwise present. The combined ABC‐spectral formulation enables one to obtain extremely accurate solutions of wave problems in unbounded domains. This is demonstrated via a number of numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.