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Abstract
Implicit finite difference schemes for the 3D wave equation using
a 27point stencil on the cubic grid are presented, for use in room
acoustics modelling and artificial reverberation. The system of
equations that arises from the implicit formulation is solved using
the Jacobi iterative method. Numerical dispersion is analysed
and computational efficiency is compared to secondorder accurate 27point explicit schemes. Timing results from GPU implementations demonstrate that the proposed algorithms scale over their explicit counterparts as expected: by a factor of M + 2, where M is a fixed number of Jacobi iterations (eight can be sufficient in single precision). Thus, the accuracy of the approximation can be improved over explicit counterparts with only a linear increase in computational costs, rather than the quartic (in operations) and cubic (in memory) increases incurred when oversampling the grid. These implicit schemes are advantageous in situations where less than 1% dispersion error is desired.
a 27point stencil on the cubic grid are presented, for use in room
acoustics modelling and artificial reverberation. The system of
equations that arises from the implicit formulation is solved using
the Jacobi iterative method. Numerical dispersion is analysed
and computational efficiency is compared to secondorder accurate 27point explicit schemes. Timing results from GPU implementations demonstrate that the proposed algorithms scale over their explicit counterparts as expected: by a factor of M + 2, where M is a fixed number of Jacobi iterations (eight can be sufficient in single precision). Thus, the accuracy of the approximation can be improved over explicit counterparts with only a linear increase in computational costs, rather than the quartic (in operations) and cubic (in memory) increases incurred when oversampling the grid. These implicit schemes are advantageous in situations where less than 1% dispersion error is desired.
Original language  English 

Title of host publication  Proceedings of the 17th International Conference on Digital Audio Effects 
Number of pages  8 
Publication status  Published  Sep 2014 
Event  17th International Conference on Digital Audio Effects  Erlangen, Germany Duration: 1 Sep 2014 → 5 Sep 2014 
Conference
Conference  17th International Conference on Digital Audio Effects 

Country/Territory  Germany 
City  Erlangen 
Period  1/09/14 → 5/09/14 
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Dive into the research topics of 'Revisiting Implicit Finite Difference Schemes for ThreeDimensional Room Acoustics Simulations'. Together they form a unique fingerprint.Projects
 1 Finished

NESS  Listening to the future: Nextgeneration Sound Synthesis through Simulation
1/01/12 → 31/12/16
Project: Research