Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method

SUMMARY Acoustic wave propagation in heterogeneous media is a topic of significant interest in many areas of science and engineering, including aeroacoustics and sound propagation in oceans. In the present work, numerical frequency domain models based on the joint use of the method of fundamental solutions and of the radial basis function collocation method (also known as Kansa's method) are discussed. In this context, the method of fundamental solutions is used to model the homogeneous part of the propagation domain, while Kansa's method is employed to model the presence of heterogeneities. The coupling between the two parts of the propagation domain is performed iteratively, allowing independent spatial discretization between the different subdomains of the model (i.e. matching collocation points at common surfaces are not necessary). Additionally, an optimised algorithm, based on the use of a varying relaxation parameter, is employed to speed up and/or to ensure the convergence of the iterative coupling process. At the end of the paper, numerical results illustrate the applicability and potentialities of the proposed formulations. Copyright © 2011 John Wiley & Sons, Ltd.

[1]  António Tadeu,et al.  Defining an accurate MFS solution for 2.5D acoustic and elastic wave propagation , 2009 .

[2]  E. Kansa.  Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates , 1990 .

[3]  Charbel Farhat,et al.  A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers , 2009 .

[4]  António Tadeu.  BENCHMARK SOLUTIONS FOR 3-D SCATTERING FROM CYLINDRICAL INCLUSIONS , 2001 .

[5]  Yan Bo,et al.  A DOMAIN DECOMPOSITION ALGORITHM WITH FINITE ELEMENT-BOUNDARY ELEMENT COUPLING , 2006 .

[6]  Paulo Amado Mendes,et al.  Wave propagation in cracked elastic slabs and half-space domains—TBEM and MFS approaches , 2007 .

[7]  Scott A. Sarra,et al.  A random variable shape parameter strategy for radial basis function approximation methods , 2009 .

[8]  Ben T. Zinn,et al.  An exact solution for one-dimensional acoustic fields in ducts with an axial temperature gradient , 1995 .

[9]  Lothar Gaul,et al.  Fast BEM-FEM mortar coupling for acoustic-structure interaction , 2005 .

[10]  E. Kansa.  MULTIQUADRICS--A SCATTERED DATA APPROXIMATION SCHEME WITH APPLICATIONS TO COMPUTATIONAL FLUID-DYNAMICS-- II SOLUTIONS TO PARABOLIC, HYPERBOLIC AND ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS , 1990 .

[11]  O. von Estorff,et al.  Iterative coupling of BEM and FEM for nonlinear dynamic analyses , 2004 .

[12]  Delfim Soares,et al.  Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method , 2006, J. Comput. Phys..

[13]  Wael Elleithy,et al.  Iterative coupling of BE and FE methods in elastostatics , 2001 .

[14]  Bruno Després,et al.  A Domain Decomposition Method for the Helmholtz equation and related Optimal Control Problems , 1996 .

[15]  Delfim Soares,et al.  A FEM-BEM coupling procedure to model the propagation of interacting acoustic-acoustic/acoustic-elastic waves through axisymmetric media , 2008 .

[16]  Bert Pluymers,et al.  Trefftz-Based Methods for Time-Harmonic Acoustics , 2007 .

[17]  O. von Estorff,et al.  Efficient non‐linear solid–fluid interaction analysis by an iterative BEM/FEM coupling , 2005 .

[18]  何银年,et al.  Fourier analysis of Schwarz domain decomposition methods for the biharmonic equation , 2009 .

[19]  Delfim Soares,et al.  A Time-Domain FEM-BEM Iterative Coupling Algorithm to Numerically Model the Propagation of Electromagnetic Waves , 2008 .

[20]  Charbel Farhat,et al.  Iterative solution of large‐scale acoustic scattering problems with multiple right hand‐sides by a domain decomposition method with Lagrange multipliers , 2001 .

[21]  S. Marburg,et al.  Computational acoustics of noise propagation in fluids : finite and boudary element methods , 2008 .

[22]  Carlos A. Felippa,et al.  Treatment of acoustic fluid-structure interaction by localized Lagrange multipliers: Formulation , 2008 .

[23]  Delfim Soares.  Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques , 2009 .

[24]  A. Ishimaru,et al.  Theory and application of wave propagation and scattering in random media , 1977, Proceedings of the IEEE.

[25]  C. S. Chen,et al.  Performance Of The BEM, MFS,And RBF Collocation Method InA 2.5D Wave Propagation Analysis , 2005 .

[26]  Gregory E. Fasshauer,et al.  On choosing “optimal” shape parameters for RBF approximation , 2007, Numerical Algorithms.

[27]  C. Farhat,et al.  Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems , 2000 .

[28]  Delfim Soares,et al.  Non-linear elastodynamic analysis by the BEM : an approach based on the iterative coupling of the D-BEM and TD-BEM formulations , 2005 .

[29]  E. Kansa,et al.  Exponential convergence and H‐c multiquadric collocation method for partial differential equations , 2003 .

[30]  Jr. Delfim Soares,et al.  An optimised FEM-BEM time-domain iterative coupling algorithm for dynamic analyses , 2008 .

[31]  Graeme Fairweather,et al.  The method of fundamental solutions for elliptic boundary value problems , 1998, Adv. Comput. Math..

[32]  António Tadeu,et al.  3D sound scattering by rigid barriers in the vicinity of tall buildings , 2001 .

[33]  E. Kansa,et al.  Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations , 2000 .

[34]  Xin Li,et al.  Trefftz Methods for Time Dependent Partial Differential Equations , 2004 .

[35]  Evert C. Lawton,et al.  An iterative finite element-boundary element algorithm , 1996 .