Tutorial on finite-difference time-domain (FDTD) methods for room acoustics simulation

2021 ◽  
Vol 149 (4) ◽  
pp. A92-A93
Author(s):  
Brian Hamilton
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Room Acoustics ◽  
Fdtd Methods ◽  
Difference Time

scholarly journals From Time-Collocated to Leapfrog Fundamental Schemes for ADI and CDI FDTD Methods

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 23
Author(s):  
Eng Leong Tan
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Unconditionally Stable ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Fdtd Methods ◽  
Difference Time

The leapfrog schemes have been developed for unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method, and recently the complying-divergence implicit (CDI) FDTD method. In this paper, the formulations from time-collocated to leapfrog fundamental schemes are presented for ADI and CDI FDTD methods. For the ADI FDTD method, the time-collocated fundamental schemes are implemented using implicit E-E and E-H update procedures, which comprise simple and concise right-hand sides (RHS) in their update equations. From the fundamental implicit E-H scheme, the leapfrog ADI FDTD method is formulated in conventional form, whose RHS are simplified into the leapfrog fundamental scheme with reduced operations and improved efficiency. For the CDI FDTD method, the time-collocated fundamental scheme is presented based on locally one-dimensional (LOD) FDTD method with complying divergence. The formulations from time-collocated to leapfrog schemes are provided, which result in the leapfrog fundamental scheme for CDI FDTD method. Based on their fundamental forms, further insights are given into the relations of leapfrog fundamental schemes for ADI and CDI FDTD methods. The time-collocated fundamental schemes require considerably fewer operations than all conventional ADI, LOD and leapfrog ADI FDTD methods, while the leapfrog fundamental schemes for ADI and CDI FDTD methods constitute the most efficient implicit FDTD schemes to date.

scholarly journals Parallelization of the finite-difference time-domain method for room acoustics modelling based on CUDA

2013 ◽  
Vol 57 (7-8) ◽  
pp. 1822-1831 ◽  
Author(s):  
José J. López ◽  
Diego Carnicero ◽  
Néstor Ferrando ◽  
José Escolano
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Time Domain Method ◽  
Room Acoustics ◽  
Domain Method ◽  
Difference Time

Optimal error estimates of finite difference time domain methods for the Klein–Gordon–Dirac system

2018 ◽  
Vol 40 (2) ◽  
pp. 1266-1293 ◽  
Author(s):  
Wenfan Yi ◽  
Yongyong Cai
Keyword(s):  
Finite Difference ◽  
Error Estimates ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Finite Difference Methods ◽  
Optimal Error Estimates ◽  
Convergence Results ◽  
Klein Gordon ◽  
Fdtd Methods ◽  
Difference Time

Abstract We propose and analyze finite difference methods for solving the Klein–Gordon–Dirac (KGD) system. Due to the nonlinear coupling between the complex Dirac ‘wave function’ and the real Klein–Gordon field, it is a great challenge to design and analyze numerical methods for KGD. To overcome the difficulty induced by the nonlinearity, four implicit/semi-implicit/explicit finite difference time domain (FDTD) methods are presented, which are time symmetric or time reversible. By rigorous error estimates, the FDTD methods converge with second-order accuracy in both spatial and temporal discretizations, and numerical results in one dimension are reported to support our conclusion. The error analysis relies on the energy method, the special nonlinear structure in KGD and the mathematical induction. Thanks to tensor grids and discrete Sobolev inequalities, our approach and convergence results are valid in higher dimensions under minor modifications.

ACOUSTIC EQUATIONS IN THE PRESENCE OF RIGID POROUS MATERIALS ADAPTED TO THE FINITE-DIFFERENCE TIME-DOMAIN METHOD

2007 ◽  
Vol 15 (02) ◽  
pp. 255-269 ◽  
Author(s):  
JOSÉ ESCOLANO ◽  
BASILIO PUEO
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Propagation Speed ◽  
Room Acoustics ◽  
Fibrous Materials ◽  
Sound Waves ◽  
Virtual Acoustics ◽  
Difference Time

Finite-difference time-domain (FDTD) method has been successfully developed to model electromagnetic systems in recent years. Since acoustics and electromagnetism share certain undulatory properties, a natural adaptation of this technique has been developed too. Several acoustics problems, such as room acoustics, require the use of fibrous tangles to attenuate the propagation speed of sound waves. Notwithstanding, although free air acoustic propagation is known, FDTD technique is not developed yet to model fibrous materials. To characterize this behavior, only a few and measurable set of parameters must be considered. In this paper, a new approach for modeling fibrous materials analysis using FDTD is presented and validated. A set of simulations covering various packing densities of a real fibrous material is performed. Loudspeaker cabinets, virtual acoustics and room acoustics are situations in which this method can be applied.

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