A Time-Domain Iteration Method for Acoustic Scattering Problems

2006 ◽  
Vol 50 (04) ◽  
pp. 334-343
Author(s):  
Jui-Hsiang Kao ◽  
Young-Zehr Kehr
Keyword(s):  
Time Domain ◽  
Iteration Method ◽  
Present Method ◽  
Domain Boundary ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Iteration Process ◽  
Scattering Problems ◽  
Retarded Time ◽  
Sharp Edges

This paper presents a new time-domain iteration method for computing multifrequency scattering waves from underwater obstacles. The equations are expressed in some forms relative to the retarded time, and the solution of scattering potential can be computed by an iteration process in which the boundary condition on each panel is naturally satisfied. Thus, the present method can treat the scattering problem of geometries with multiple sharp edges. In addition, the numerical inaccuracy due to time interpolation is minimized by using a Fourier series, and the results can robustly converge to correct values by setting zero initial scattering potentials. Several cases of a half sphere in different frequency ranges and one of multifrequency were tested by the present method. The results of all these cases agree with those reached by a frequency-domain boundary element method (BEM). In addition, a case with multiple sharp edges is also tested. The converged results can be obtained by the present method, but not by the BEM. Moreover, the present method is more computationally efficient, especially for the multifrequency case.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

scholarly journals Reconstruction of transient pressure and acceleration over a tire surface using the inverse time domain boundary element method

2019 ◽  
Vol 283 ◽  
pp. 04014
Author(s):  
Yang Zhang ◽  
Chuanxing Bi ◽  
Xiaozheng Zhang ◽  
Yongbin Zhang ◽  
Liang Xu
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Sound Field ◽  
Rigid Sphere ◽  
Transient Pressure ◽  
Retarded Time ◽  
Reconstructed Surface ◽  
Element Method

The inverse time domain boundary element method (ITBEM) that is derived from the direct time domain boundary element method by eliminating the retarded time is able to reconstruct the transient pressure and flux on the surface of an arbitrarily shaped source by measuring the pressure on a hologram surface. In the present work, the ITBEM is applied to reconstruct the transient pressure and acceleration over the surface of a tire which is supported away from the ground in a semi-anechoic chamber. The tire is impacted by a rigid sphere to generate a transient sound field, and the measurement is controlled by a trigger which is connected to an acceleration sensor stuck on the surface of the tire. The pressure and acceleration on the surface of the tire are reconstructed from the holographic pressure measured by array microphones. By visualizing the pressure and acceleration with respect to the elapsed time, the wave propagation phenomenon of the pressure and acceleration on the surface of the tire is shown clearly. The comparison of the reconstructed surface acceleration to the measured one demonstrates the effectiveness of ITBEM for transient sound field reconstruction.

scholarly journals A time domain sampling method for inverse acoustic scattering problems

2016 ◽  
Vol 314 ◽  
pp. 647-660 ◽  
Author(s):  
Yukun Guo ◽  
Dietmar Hömberg ◽  
Guanghui Hu ◽  
Jingzhi Li ◽  
Hongyu Liu
Keyword(s):  
Time Domain ◽  
Sampling Method ◽  
Acoustic Scattering ◽  
Scattering Problems ◽  
Acoustic Scattering Problems

A Domain Embedding Method for Scattering Problems with an Absorbing Boundary or a Perfectly Matched Layer

2003 ◽  
Vol 11 (02) ◽  
pp. 159-174 ◽  
Author(s):  
Erkki Heikkola ◽  
Tuomo Rossi ◽  
Jari Toivanen
Keyword(s):  
Scattering Problem ◽  
Acoustic Scattering ◽  
Partial Solution ◽  
Perfectly Matched Layer ◽  
Dimensional Subspace ◽  
Equation Modeling ◽  
Solution Technique ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Embedding Method

The efficient numerical solution of the exterior Helmholtz equation modeling the acoustic scattering by an obstacle is considered. The exterior problem is approximated by truncating the domain with a rectangular boundary and using either a perfectly matched layer or a second-order absorbing boundary condition to reduce reflections from the artificial boundary. The scattering problem is solved iteratively by using a domain embedding method with an efficient separable preconditioner. With this approach, it is possible to realize the GMRES iterations in a low-dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner. The accuracy and the efficiency of the proposed solution technique are studied with numerical experiments.

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