A Beam-Tracing Domain Decomposition Method for Sound Holography in Church Acoustics

In this paper, an original beam-tracing domain decomposition method is proposed for church acoustics. This new method allows to analyze large-scale acoustics problems in a reasonnable time on parallel architectures. Numerical experiments, for sound holography within the church of the Royaumont abbey, illustrate the performance of the proposed beam-tracing domain decomposition method on multi-cores and multi-processors architectures.

[1]  David S. Burnett,et al.  An ellipsoidal acoustic infinite element , 1998 .

[2]  S. Ghanemi,et al.  A Domain Decomposition Method for Helmholtz Scattering Problems , 1997 .

[3]  D. Botteldooren,et al.  Prediction-step staggered-in-time FDTD: An efficient numerical scheme to solve the linearised equations of fluid dynamics in outdoor sound propagation , 2007 .

[4]  D. Botteldooren Finite‐difference time‐domain simulation of low‐frequency room acoustic problems , 1995 .

[5]  Frédéric Magoulès,et al.  Algebraic Dirichlet-to-Neumann mapping for linear elasticity problems with extreme contrasts in the coefficients , 2006 .

[6]  Leif Kobbelt,et al.  Simulation of Radio Wave Propagation by Beam Tracing , 2009, EGPGV@Eurographics.

[7]  Frédéric Magoulès,et al.  Improved ad hoc interface conditions for Schwarz solution procedure tuned to highly heterogeneous media , 2006 .

[8]  Jont B. Allen,et al.  Image method for efficiently simulating small‐room acoustics , 1976 .

[9]  L. Thompson A review of finite-element methods for time-harmonic acoustics , 2006 .

[10]  Zhao Wen-zhong,et al.  Research on acoustic-structure sensitivity using FEM and BEM , 2007 .

[11]  Y. Maday,et al.  Optimized Schwarz methods without overlap for highly heterogeneous media , 2007 .

[12]  Samuli Laine,et al.  Accelerated beam tracing algorithm , 2009 .

[13]  Jaroslav Kruis Domain Decomposition Methods for Distributed Computing , 2007 .

[14]  Frédéric Magoulès,et al.  Analysis of a conjugated infinite element method for acoustic scattering , 2007 .

[15]  Philipp Slusallek,et al.  State of the Art in Interactive Ray Tracing , 2001, Eurographics.

[16]  Tomas Akenine-Möller,et al.  Fast, minimum storage ray/triangle intersection , 1997, J. Graphics, GPU, & Game Tools.

[17]  Frédéric Magoulès,et al.  NUMERICAL ANALYSIS OF A COUPLED FINITE-INFINITE ELEMENT METHOD FOR EXTERIOR HELMHOLTZ PROBLEMS , 2006 .

[18]  Frédéric Magoulès,et al.  Approximation of Optimal Interface Boundary Conditions for Two-Lagrange Multiplier FETI Method , 2005 .

[19]  Barry Smith,et al.  Domain Decomposition Methods for Partial Differential Equations , 1997 .

[20]  Thomas Funkhouser,et al.  A beam tracing method for interactive architectural acoustics. , 2004, The Journal of the Acoustical Society of America.

[21]  Frédéric Magoulès,et al.  Algebraic approximation of Dirichlet-to-Neumann maps for the equations of linear elasticity , 2006 .

[22]  Frédéric Magoulès,et al.  ALGEBRAIC WAY TO DERIVE ABSORBING BOUNDARY CONDITIONS FOR THE HELMHOLTZ EQUATION , 2005 .

[23]  Barry F. Smith,et al.  Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations , 1996 .

[24]  Andrea Toselli,et al.  Domain decomposition methods : algorithms and theory , 2005 .

[25]  I. Harari,et al.  Numerical investigations of stabilized finite element computations for acoustics , 2004 .

[26]  Soon-Wook Kwon,et al.  Fitting range data to primitives for rapid local 3D modeling using sparse range point clouds , 2004 .

[27]  Frédéric Magoulès,et al.  Convergence analysis of Schwarz methods without overlap for the Helmholtz equation , 2004 .

[28]  Tapio Lokki,et al.  Implementation and Visualization of Edge Diffraction with Image-source Method , 2002 .

[29]  Frédéric Magoulès,et al.  Non-overlapping additive Schwarz methods tuned to highly heterogeneous media , 2005 .

[30]  Frédéric Magoulès,et al.  Algebraic approach to absorbing boundary conditions for the Helmholtz equation , 2007, Int. J. Comput. Math..

[31]  Frédéric Nataf,et al.  Symmetrized Method with Optimized Second-Order Conditions for the Helmholtz Equation , 1998 .

[32]  Frédéric Magoulès,et al.  Absorbing interface conditions for domain decomposition methods: A general presentation , 2006 .

[33]  Frédéric Magoulès,et al.  Studies of an infinite element method for acoustical radiation , 2006 .

[34]  Frédéric Magoulès,et al.  Lagrangian formulation of domain decomposition methods: A unified theory , 2006 .

[35]  Kellogg S. Booth,et al.  Report from the chair , 1986 .

[36]  F. Magoulès,et al.  An optimized Schwarz method with two‐sided Robin transmission conditions for the Helmholtz equation , 2007 .

[37]  F. Ihlenburg Finite Element Analysis of Acoustic Scattering , 1998 .

[38]  Markus Wagner,et al.  Interactive Rendering with Coherent Ray Tracing , 2001, Comput. Graph. Forum.

[39]  J.-S. Sun,et al.  A Generalized Infinite Element for Acoustic Radiation , 2005 .