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High‐order doubly asymptotic open boundaries for scalar wave equation
Author(s) -
Prempramote Suriyon,
Song Chongmin,
TinLoi Francis,
Lin Gao
Publication year - 2009
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.2562
Subject(s) - mathematical analysis , mathematics , scalar (mathematics) , method of matched asymptotic expansions , ordinary differential equation , scalar field , asymptotic analysis , asymptotic expansion , differential equation , geometry , mathematical physics
High‐order doubly asymptotic open boundaries are developed for transient analyses of scalar waves propagating in a semi‐infinite layer with a constant depth and a circular cavity in a full‐plane. The open boundaries are derived in the frequency domain as doubly asymptotic continued fraction solutions of the dynamic stiffness of the unbounded domains. Each term of the continued fraction is a linear function of the excitation frequency. The constants of the continued fraction solutions are determined recursively. The continued fraction solution is expressed in the time domain as ordinary differential equations, which can be solved by standard time‐stepping schemes. No parameters other than the orders of the low‐ and high‐frequency expansions need to be selected by users. Numerical experiments demonstrate that evanescent waves and long‐time (low‐frequency) responses are simulated accurately. In comparison with singly asymptotic open boundaries, significant gain in accuracy is achieved at no additional computational cost. Copyright © 2009 John Wiley & Sons, Ltd.