Elimination of a non-oscillatory instability in a retarded potential integral equation

作者: Jean-Marc Parot , Christophe Thirard , Christian Puillet

DOI: 10.1016/J.ENGANABOUND.2006.09.014

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摘要: Abstract This paper deals with the unstable behaviour of an acoustic boundary element model. The model, based on a marching time (MOT) algorithm, uses hypersingular derivative Green method. It is able to cope open or closed diffracting objects. These objects are rigid can be deformed. When long enough computation carried out, pressure magnitude shows exponential growth, which unrealistic behaviour. In we show that faced numerical instability static in cavities. A simple processing method using eigenelement decomposition ‘ad hoc’ matrix suffices correct problem without damage other components result. related more general dedicated problems.

参考文章(19)
Françoise Chatelin, Spectral approximation of linear operators Society for Industrial and Applied Mathematics. ,(2011) , 10.1137/1.9781611970678
S. Amini, S.M. Kirkup, Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods Journal of Computational Physics. ,vol. 118, pp. 208- 221 ,(1995) , 10.1006/JCPH.1995.1093
M. J. BLUCK, S. P. WALKER, ANALYSIS OF THREE-DIMENSIONAL TRANSIENT ACOUSTIC WAVE PROPAGATION USING THE BOUNDARY INTEGRAL EQUATION METHOD International Journal for Numerical Methods in Engineering. ,vol. 39, pp. 1419- 1431 ,(1996) , 10.1002/(SICI)1097-0207(19960430)39:8<1419::AID-NME911>3.0.CO;2-C
Y. Kawai, T. Terai, A numerical method for the calculation of transient acoustic scattering from thin rigid plates Journal of Sound and Vibration. ,vol. 141, pp. 83- 96 ,(1990) , 10.1016/0022-460X(90)90514-Z
F.C. Araújo, D.R. Alberto, C. Dors, Analysis of 3D time-dependent acoustic problems via a generic BE substructuring algorithm based on iterative solvers Engineering Analysis With Boundary Elements. ,vol. 27, pp. 705- 716 ,(2003) , 10.1016/S0955-7997(03)00021-3
B.P. Rynne, P.D. Smith, Stability of Time Marching Algorithms for the Electric Field Integral Equation Journal of Electromagnetic Waves and Applications. ,vol. 4, pp. 1181- 1205 ,(1990) , 10.1163/156939390X00762
Penny J. Davies, Dugald B. Duncan, Averaging techniques for time-marching schemes for retarded potential integral equations Applied Numerical Mathematics. ,vol. 23, pp. 291- 310 ,(1997) , 10.1016/S0168-9274(96)00069-4
A. A. Ergin, Balasubramaniam Shanker, Eric Michielssen, Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm Journal of the Acoustical Society of America. ,vol. 106, pp. 2405- 2416 ,(1999) , 10.1121/1.428077
R. Jeans, I.C. Mathews, A comparison of numerical collocation and variational procedures to the hypersingular acoustic integral operator Computer Methods in Applied Mechanics and Engineering. ,vol. 101, pp. 5- 26 ,(1992) , 10.1016/0045-7825(92)90012-9