Scalar wave equation by the boundary element method: A D‐BEM approach with constant time‐weighting functions

Carrer, J. A. M.; Mansur, Webe João

doi:10.1002/nme.2732

Cited by 14 publications

(12 citation statements)

References 27 publications

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“…This problem has been also introduced in the works of Noh et al and Carrer and Mansur while presenting the exact solution as

u ((), x, t) = \frac{8}{π^{2}} \frac{PL}{EA} \sum_{k = 1}^{\infty} \frac{{((), - 1)}^{k - 1}}{{((), 2 k - 1)}^{2}} \sin ((), \frac{(2 k - 1) π italicx}{2 L}) ((), 1 - \cos ((), \frac{((), 2 k - 1) π}{2 L} \sqrt{\frac{E}{ρ}} t)),

where E and ρ are the elasticity module and the density of the material, respectively, which are considered unity leading to wave speed as c = 1 m/s. Also in and , L is the bar's length.…”

Section: Numerical Resultsmentioning

confidence: 99%

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

Movahedian

Boroomand

Mansouri

2018

Numerical Meth Engineering

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Summary In this paper, a new effective boundary node method is presented for the solution of acoustic problems, directly in time domain, using exponential basis functions. Unlike many other methods using boundary information, the final coefficient matrix is sparse. The formulation is well suited for domains whose extent is relatively larger than the distance traveled by the acoustic wave in an increment of time. The exponential basis functions used satisfy the time‐space governing equation. This helps to choose a relatively large time increment and a moderate number of boundary points, which leads to reduction of computation time. The computation is performed incrementally using a weighted residual in time. Through a series of numerical examples, it is shown that the method, when combined with a domain decomposition strategy, is effectively capable of solving various 1‐ to 3‐dimensional acoustic problems.

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“…This problem has been also introduced in the works of Noh et al and Carrer and Mansur while presenting the exact solution as

u ((), x, t) = \frac{8}{π^{2}} \frac{PL}{EA} \sum_{k = 1}^{\infty} \frac{{((), - 1)}^{k - 1}}{{((), 2 k - 1)}^{2}} \sin ((), \frac{(2 k - 1) π italicx}{2 L}) ((), 1 - \cos ((), \frac{((), 2 k - 1) π}{2 L} \sqrt{\frac{E}{ρ}} t)),

where E and ρ are the elasticity module and the density of the material, respectively, which are considered unity leading to wave speed as c = 1 m/s. Also in and , L is the bar's length.…”

Section: Numerical Resultsmentioning

confidence: 99%

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

Movahedian

Boroomand

Mansouri

2018

Numerical Meth Engineering

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“…For problems such as stress concentration or infinite domains, BEM can be applied to achieve better accuracy in comparison with finite element method. Many usages of BEM in solving problems related to wave propagation, crack, buckling, optimization, etc are reported in the literature …”

Section: Introductionmentioning

confidence: 99%

The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element framework

Hamzehei‐Javaran

Shojaee²

2017

Numerical Meth Engineering

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In this paper, new spherical Hankel shape functions are used to reformulate boundary element method for 2-dimensional elastostatic and elastodynamic problems. To this end, the dual reciprocity boundary element method is reconsidered by using new spherical Hankel shape functions to approximate the state variables (displacements and tractions) of Navier's differential equation. Using enrichment of a class of radial basis functions (RBFs), called spherical Hankel RBFs hereafter, the interpolation functions of a Hankel boundary element framework has been derived. For this purpose, polynomial terms are added to the functional expansion that only uses spherical Hankel RBF in the approximation. In addition to polynomial function fields, the participation of spherical Bessel function fields has also increased robustness and efficiency in the interpolation. It is very interesting that there is no Runge phenomenon in equispaced Hankel macroelements, unlike equispaced classic Lagrange ones. Several numerical examples are provided to demonstrate the effectiveness, robustness and accuracy of the proposed Hankel shape functions and in comparison with the classic Lagrange ones, they show much more accurate and stable results. KEYWORDS 2D elastostatic and elastodynamic problems, boundary element method, dual reciprocity method, equispaced macroelements, Runge phenomenon, spherical Hankel shape functions | INTRODUCTIONElastostatics and elastodynamics illustrate a wide range of phenomena in engineering and physical problems such as force equilibrium of special structures and analysis of structures under vibratory motor, earthquake, explosion, and collision loads, where wave propagation is expressed by a governing linear partial differential equation, associated with suitable boundary and initial conditions. Generally, finding the solution of elastostatic and elastodynamic problems for analysis and design purposes through analytical approaches can be hard and time-consuming. Also, with a little complexity in boundary conditions, analytical solution may even become impossible. Therefore, in most practical engineering cases, solving them numerically seems to be inevitable. One of the numerical methods that have been considered significantly by researchers is boundary element method (BEM). 1,2 As it is clear from its name, boundary element only needs the boundary to be discretized, and it is not necessary to discretize the domain in this method. This matter leads to the reduction of unknowns to be stored. Therefore, less computational cost and storage space will be spent. For problems such as stress concentration or infinite domains, BEM can

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“…The primary methods for forward modeling with topography mainly include the boundary element (Perrey-Debain et al, 2004;Carrer and Mansur, 2010), finite element (Ke et al, 2001) and finite difference methods. Among them, the boundary element and finite element methods are most adaptable to irregular surfaces.…”

Section: Introductionmentioning

confidence: 99%

Multisource Full Waveform Inversion with Topography Using Ghost Extrapolation

Zhang

Zhan

Dai

et al. 2012

International Geophysical Conference and Oil &Amp; Gas Exhibition, Istanbul, Turkey, 17-19 September 2012

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Standard finite-difference modeling of the wave equation for models with severe topographic changes in elevation generates artificial diffractions in the synthetic traces. This can lead to unacceptable inaccuracies in the velocity tomogram computed by full waveform inversion (FWI). To alleviate this problem we propose a polynomial interpolation of the field values at and near the irregular free surface. This improved finite-difference procedure is denoted as the ghost extrapolation method. To validate its effectiveness, synthetic data are computed from a Marmousi model with severe topographical variations of the free surface. These data are inverted using both the standard FWI and the phase-encoded multisource FWI methods. Results show the ghost extrapolation method is effective in eliminating noticeable artifacts and producing accurate tomograms.

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Scalar wave equation by the boundary element method: A D‐BEM approach with constant time‐weighting functions

Cited by 14 publications

References 27 publications

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

A robust time‐space formulation for large‐scale scalar wave problems using exponential basis functions

The solution of elastostatic and dynamic problems using the boundary element method based on spherical Hankel element framework

Multisource Full Waveform Inversion with Topography Using Ghost Extrapolation

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