An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems

Falletta, Silvia; Monegato, Giovanni; Scuderi, Letizia

doi:10.1007/s11565-022-00420-x

Cited by 1 publication

(2 citation statements)

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“…Based on the potential theories, the retarded single-layer potential of (1.1) is introduced by (see [15], [27] for instance)…”

Section: 1mentioning

confidence: 99%

“…To solve the RPBIE of (1.1) numerically, due to the convolution quadrature method (CQM) that developed by Lubich [26]- [28], researchers have proposed many numerical methods, including the CQM in time and the BEM in space (see [4], [6]- [9], [14], [23], [27], [32] for instance), the collocation method in space (see [15], [29]), and the trigonometric interpolation method in space [38]. In [2],…”

Section: Introductionmentioning

confidence: 99%

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Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems

Guo,

Huang,

et al. 2024

Preprint

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This paper studies the time domain acoustic wave scattering problems of a bounded obstacle or a smooth open arc in the unbounded domain, where the obstacle has the smooth and closed boundary. Due to the potential theories, the first kind retarded single-layer potential boundary integral equations of the above problems can be obtained and they are solved by two steps, we get the temporal discretization by the convolution quadrature method firstly, and then the first kind boundary integral equations in space are solved by the quadrature method. Meanwhile, the scattered field can be computed in terms of the trapezoidal rule. The existence and uniqueness of the numerical solution are proved, the convergence of the approximate solution is also analysed and the error bound is got. The asymptotic expansion of the error in space shows that the convergence rate is O(h3). Moreover, the extrapolation algorithm is used to improve the accuracy of the numerical solution. The posteriori error estimate is also obtained, which is helpful for designing the self-adaptive algorithm. Some numerical experiments are implemented to show the effectiveness of our method.

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“…Based on the potential theories, the retarded single-layer potential of (1.1) is introduced by (see [15], [27] for instance)…”

Section: 1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems

Guo,

Huang,

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

An overview on a time discrete convolution—space collocation BEM for 2D exterior wave propagation problems

Cited by 1 publication

References 36 publications

Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems

Quadrature method and extrapolation algorithm for solving the boundary integral equations of the acoustic wave scattering problems

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