scholarly journals A priori error estimates for a time-dependent boundary element method for the acoustic wave equation in a half-space

2014 ◽  
Vol 40 (2) ◽  
pp. 448-462 ◽  
Author(s):  
Heiko Gimperlein ◽  
Zouhair Nezhi ◽  
Ernst P. Stephan
Keyword(s):  
Wave Equation ◽  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Error Estimates ◽  
A Priori ◽  
Time Dependent ◽  
Acoustic Wave Equation ◽  
Priori Error Estimates

Obtaining three‐dimensional velocity information directly from reflection seismic data: An inverse scattering formalism

Geophysics ◽  
1981 ◽  
Vol 46 (8) ◽  
pp. 1116-1120 ◽  
Author(s):  
A. B. Weglein ◽  
W. E. Boyse ◽  
J. E. Anderson
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Inverse Scattering ◽  
Seismic Data ◽  
A Priori ◽  
Three Dimensional ◽  
Quantum Scattering ◽  
Acoustic Wave Equation ◽  
Reflection Seismic ◽  
The One

We present a formalism for obtaining the subsurface velocity configuration directly from reflection seismic data. Our approach is to apply the results obtained for inverse problems in quantum scattering theory to the reflection seismic problem. In particular, we extend the results of Moses (1956) for inverse quantum scattering and Razavy (1975) for the one‐dimensional (1-D) identification of the acoustic wave equation to the problem of identifying the velocity in the three‐dimensional (3-D) acoustic wave equation from boundary value measurements. No a priori knowledge of the subsurface velocity is assumed and all refraction, diffraction, and multiple reflection phenomena are taken into account. In addition, we explain how the idea of slant stack in processing seismic data is an important part of the proposed 3-D inverse scattering formalism.

A Fast Multipole Boundary Element Method for Three-Dimensional Half-Space Acoustic Wave Problems Over an Impedance Plane

2015 ◽  
Vol 12 (01) ◽  
pp. 1350090 ◽  
Author(s):  
Haijun Wu ◽  
Yijun Liu ◽  
Weikang Jiang ◽  
Wenbo Lu
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Three Dimensional ◽  
The Real ◽  
Impedance Plane ◽  
Real Domain ◽  
Wave Problems ◽  
Element Method

A high-frequency fast multipole boundary element method (FMBEM) based on the Burton–Miller formulation is proposed for three-dimensional acoustic wave problems over an infinite plane with impedance boundary conditions. The Green's function for the sound propagation over an impedance plane is employed explicitly in the boundary integral equation (BIE). To deal with the integral appearing in the half-space Green's function, the downward pass in the FMBEM is divided into two parts to compute contributions from the real domain to the real and image domains, respectively. A piecewise analytical method is proposed to compute the moment-to-local (M2L) translator from the real domain to the image domain accurately. An algorithm based on the multi-level tree structure is designed to compute the M2L translators efficiently. Correspondingly, the direct coefficient can also be computed efficiently by taking advantage of the algorithm of the efficient M2L. A flexible generalized minimal residual (fGMRES) is applied to accelerating the solution when the convergence is very slow. Numerical examples are presented to demonstrate the accuracy and efficiency of the developed FMBEM. Good solutions and high acceleration ratios compared with the conventional boundary element method clearly show the potential of the FMBEM for large-scale 3D acoustic wave problems over an infinite impedance plane which are of practical significance.

Fast Multipole Boundary Element Method for 3-D Full- and Half-Space Acoustic Wave Problems

2009 ◽  
Author(s):  
Yijun Liu ◽  
Milind Bapat
Keyword(s):  
Boundary Element Method ◽  
Acoustic Wave ◽  
Boundary Element ◽  
Half Space ◽  
Large Scale ◽  
Fast Multipole ◽  
Wave Problems ◽  
Acoustic Bem ◽  
Element Method

In this paper, the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 3-D full- and half-space domains will be discussed. First, the fast multipole BEM formulations will be presented and then improvements to the formulations and algorithms will be discussed. Examples with large-scale acoustic BEM models, with the DOFs above 2 millions and solved on desktop PCs, will be presented to demonstrate the potential of the fast multipole BEM for modeling large-scale structural acoustic problems.

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