Explicit Higher-Order FDTD Schemes for 3D Room Acoustic Simulation

The Finite Difference Time Domain method is gaining popularity as a means to simulate and solve room acoustical problems. In this paper, a new set of stencils is defined that approximate the wave equation with a high degree of accuracy and lower dispersion error. Compared to the previously presented optimal scheme, the Interpolated Wideband scheme, our schemes are computationally less demanding and more practical to implement. They use at least 8 times less memory for the same audio rate and are an order of magnitude faster, although the former has a higher valid bandwidth. Despite their larger computational expense per node update, it is shown that our schemes on the whole use less memory and computation time than the Standard Rectilinear stencil, particularly when GPU implementations are employed. Lastly, a new way of visualizing and comparing valid bandwidth is recommended.

[1]  Murray Hodgson,et al.  Improved algorithms and methods for room sound-field prediction by acoustical radiosity in arbitrary polyhedral rooms. , 2004, The Journal of the Acoustical Society of America.

[2]  Stefan Bilbao,et al.  FOURTH-ORDER AND OPTIMISED FINITE DIFFERENCE SCHEMES FOR THE 2-D WAVE EQUATION , 2013 .

[3]  Wenhua. Wenhua Yu ... . Yu,et al.  Parallel Finite-Difference Time-Domain Method , 2006 .

[4]  Ming C. Lin,et al.  Efficient and Accurate Sound Propagation Using Adaptive Rectangular Decomposition , 2009, IEEE Transactions on Visualization and Computer Graphics.

[5]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[6]  Thomas A. Funkhouser,et al.  Modeling acoustics in virtual environments using the uniform theory of diffraction , 2001, SIGGRAPH.

[7]  José Escolano,et al.  Parallelization of the finite-difference time-domain method for room acoustics modelling based on CUDA , 2013, Math. Comput. Model..

[8]  Tapio Lokki,et al.  The room acoustic rendering equation. , 2007, The Journal of the Acoustical Society of America.

[9]  Wenyu Jiang,et al.  Using Programmable Graphics Hardware for Acoustics and Audio Rendering , 2009 .

[10]  Matti Karjalainen,et al.  Digital Waveguides versus Finite Difference Structures: Equivalence and Mixed Modeling , 2004, EURASIP J. Adv. Signal Process..

[11]  Tapio Lokki,et al.  Rays or Waves? Understanding the Strengths and Weaknesses of Computational Room Acoustics Modeling Techniques , 2010 .

[12]  Stefan Bilbao.  Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics , 2009 .

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

[14]  Tapio Takala,et al.  Simulation of Room Acoustics with a 3-D Finite Difference Mesh , 1994, ICMC.

[15]  Maarten van Walstijn,et al.  Room Acoustics Simulation Using 3-D Compact Explicit FDTD Schemes , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[16]  Tapio Lokki,et al.  The perceptual effects of dispersion error on room acoustic model auralization , 2011 .

[17]  Graeme Fairweather,et al.  A High Accuracy Alternating Direction Method for the Wave Equation , 1965 .

[18]  Dinesh Manocha,et al.  An efficient GPU-based time domain solver for the acoustic wave equation , 2012 .

[19]  Verification of prediction based on randomized tail‐corrected cone‐tracing and array modeling , 1999 .

[20]  M. Ciment,et al.  Higher order compact implicit schemes for the wave equation , 1975 .

[21]  George Lindfield,et al.  Numerical Methods Using MATLAB , 1998 .

[22]  Julius O. Smith.  Equivalence of the digital waveguide and finite difference time domain schemes , 2004 .

[23]  Vesa Välimäki,et al.  Audio Signal Processing Using Graphics Processing Units , 2011 .

[24]  R. Mittra,et al.  Parallel Finite-Difference Time-Domain Method (Artech House Electromagnetic Analysis) , 2006 .

[25]  Stefan Bilbao,et al.  Construction and optimization techniques for high order schemes for the two-dimensional wave equation , 2013 .

[26]  Ming C. Lin,et al.  Precomputed wave simulation for real-time sound propagation of dynamic sources in complex scenes , 2010, ACM Trans. Graph..

[27]  John B. Schneider,et al.  Implementation of transparent sources in FDTD simulations , 1998 .

[28]  Lauri Savioja,et al.  REAL-TIME 3D FINITE-DIFFERENCE TIME-DOMAIN SIMULATION OF LOW- AND MID-FREQUENCY ROOM ACOUSTICS , 2010 .

[29]  Stefan Bilbao,et al.  Modeling of Complex Geometries and Boundary Conditions in Finite Difference/Finite Volume Time Domain Room Acoustics Simulation , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[30]  T. Lokki,et al.  Diffraction modeling in acoustic radiance transfer method , 2008 .

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

[32]  Stefan Bilbao,et al.  Computing room acoustics with CUDA - 3D FDTD schemes with boundary losses and viscosity , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[33]  Thomas A. Funkhouser,et al.  A beam tracing approach to acoustic modeling for interactive virtual environments , 1998, SIGGRAPH.

[34]  Augusto Sarti,et al.  Fast Tracing of Acoustic Beams and Paths Through Visibility Lookup , 2008, IEEE Transactions on Audio, Speech, and Language Processing.

[35]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations , 1989 .

[36]  Damian T. Murphy,et al.  The KW-Boundary Hybrid Digital Waveguide Mesh for Room Acoustics Applications , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[37]  J. Strikwerda.  Finite Difference Schemes and Partial Differential Equations, Second Edition , 2004 .

[38]  Paulius Micikevicius,et al.  3D finite difference computation on GPUs using CUDA , 2009, GPGPU-2.

[39]  Vesa Välimäki,et al.  Interpolated 3-D digital waveguide mesh with frequency warping , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[40]  B. Fornberg.  Generation of finite difference formulas on arbitrarily spaced grids , 1988 .