On a way to save memory when solving time domain boundary integral equations for acoustic and vibroacoustic applications

Thirard, Christophe; Parot, Jean-Marc

doi:10.1016/j.jcp.2017.07.040

Cited by 3 publications

(1 citation statement)

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“…For instance, for March-On-in-Time (MOT) schemes, the recently developed Plane Wave Time Domain (PWTD) algorithm can be used to accelerate the far interactions [11], akin to the Fast Multipole Methods in the frequency domain. Another efficient time domain propagation algorithm is the multi-level Cartesian Non-uniform Grid Time Domain Algorithm (CNGTDA), based on the delay-and amplitude-compensated acoustic field [12][13][14]. With these breakthroughs, as well as the advances in computational power and new computing architectures, an increase in the application of time domain integral equations for unsteady aerodynamics and aeroacoustics is expected in the future.…”

Section: Introductionmentioning

confidence: 99%

On hybrid temporal basis functions for stable numerical solution of time domain boundary integral equations

2019

Adv. Aerodyn.

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Problems in unsteady aerodynamics and aeroacoustics can sometimes be formulated as integral equations, such as the boundary integral equations. Numerical discretization of integral equations in the time domain often leads to so-called March-On-in-Time (MOT) schemes. In the literature, the temporal basis functions used in MOT schemes have been largely limited to low-order shifted Lagrange basis functions. In order to evaluate the accuracy and effectiveness of the temporal basis functions, a Fourier analysis of the temporal interpolation schemes is carried out. Based on the Fourier analysis, the spectral resolutions of various temporal basis functions are quantified. It is argued that hybrid temporal basis functions be used for interpolation of the numerical solution and its derivatives with respect to time. Stability of the proposed hybrid schemes is studied by a matrix eigenvalue method. Substantial improvement in accuracy and efficiency by using the hybrid temporal basis functions for time domain integral equations is demonstrated by numerical examples. Compared with the traditional temporal basis functions, the use of hybrid basis functions keeps numerical errors low for a larger frequency range given the same time step size. Conversely, for a given range of frequency of interest, a larger time step can be used with the hybrid temporal basis functions, resulting in an increase in computational efficiency and, at the same time, a reduction in memory requirement.

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