Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering

Acosta, Sebastián; Villamizar, Vianey

doi:10.1016/j.jcp.2010.04.011

Cited by 26 publications

(41 citation statements)

References 34 publications

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“…This provides a very convenient way when one does not want to use the specific functions or need to build a more complicated operator. For example, the spectral (dense) construction of the BWIE for the Dirichlet problem can be written IntegralOperator(O, a, M modes, k, [1,2,3], [0.5, -eta, -1]);…”

Section: Defining and Solving An Integral Equationmentioning

confidence: 99%

“…The vector M modes is such that M modes(p)= N p , the argument vector [1,2,3] refers to respectively the operators Identity (1), L (2) and M (3) and the last one [0.5, -eta, -1] carries the weight to apply to each operator in the linear combination (eta must previously have taken a prescribed complex value in the script). Without entering too much into details, each block of the final global matrix can be specified thanks to this numbering (instead of a vector, a 2D-or a 3D-array is then considered as argument).…”

Section: Defining and Solving An Integral Equationmentioning

confidence: 99%

See 1 more Smart Citation

µ-diff: A matlab toolbox for multiple scattering problems by disks

Thierry¹,

Antoine²,

Chniti³

et al. 2015

AIP Conference Proceedings

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The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in µ-diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized. Some complete numerical examples of applications (direct and inverse scattering) are provided to show that µ-diff is a flexible, efficient and robust toolbox for solving some complex multiple scattering problems.

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Section: Defining and Solving An Integral Equationmentioning

confidence: 99%

Section: Defining and Solving An Integral Equationmentioning

confidence: 99%

µ-diff: A matlab toolbox for multiple scattering problems by disks

Thierry¹,

Antoine²,

Chniti³

et al. 2015

AIP Conference Proceedings

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“…19 Villamizar and Acosta have continued to develop a variety of curvilinear grids, similar to that used here, and have applied them to scattering from multiple nonconventional objects in two-dimensions. 24,25 III. NUMERICAL SIMULATION The model simulated in this work is scaled down to exactly 1 4 the size of the mathematical model used by Stepanishen and Tougas.…”

Section: Discretizationmentioning

confidence: 99%

Finite-difference simulations of transient radiation from a finite-length pipe

Tengelsen

Anderson

Villamizar

et al. 2014

The Journal of the Acoustical Society of America

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The far-field radiation originating from a finite-length pipe is well studied, especially for steady-state conditions. However, because all physical systems do not begin in steady state, these radiation characteristics are only valid after the transient portion of the solution has decayed. Understanding transient radiation characteristics may be important (particularly for systems transmitting very short-duration signals), as they can differ quite significantly. A numerical complication to this problem involves dealing with a sharp corner in the domain of interest. While many numerical studies have attempted to couple solutions from the domains inside and outside a pipe, the analysis presented in this work treats the computational domain as a single region by expressing the entire physical domain as a map from a simple rectangular domain in generalized curvilinear coordinates. This method will be introduced in detail and general results of transient radiation will be presented for an infinitely baffled, finite-length pipe using the finite-difference method expressed in generalized curvilinear coordinates. Comparison will be made to previous results [P. Stepanishen and R. A. Tougas, J. Acoust. Soc. Am. 93, 3074-3084 (1993)] that used a semi-analytic approach with certain assumptions.

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“…More precisely following [28], we assume that the obstacle in the upper half-plane is well separated from Γ. Therefore, it can be enclosed by an artificial circular boundary B with radius R, centered at a point b = (b x , b y ) inside the obstacle, which is completely contained in Ω (b y > R).…”

Section: Lemmamentioning

confidence: 99%

The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane

Acosta¹,

Villamizar²,

Malone³

2012

Computer Methods in Applied Mechanics and Engineering

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The multiple-Dirichlet-to-Neumann (multiple-DtN) non-reflecting boundary condition is adapted to acoustic scattering from obstacles embedded in the half-plane. The multiple-DtN map is coupled with the method of images as an alternative model for multiple acoustic scattering in the presence of acoustically soft and hard plane boundaries. As opposed to the current practice of enclosing all obstacles with a large semicircular artificial boundary that contains portion of the plane boundary, the proposed technique uses small artificial circular boundaries that only enclose the immediate vicinity of each obstacle in the half-plane. The adapted multiple-DtN condition is simultaneously imposed in each of the artificial circular boundaries. As a result the computational effort is significantly reduced. A computationally advantageous boundary value problem is numerically solved with a finite difference method supported on boundary-fitted grids. Approximate solutions to problems involving two scatterers of arbitrary geometry are presented. The proposed numerical method is validated by comparing the approximate and exact far-field patterns for the scattering from a single and from two circular obstacles in the half-plane.

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Coupling of Dirichlet-to-Neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering

Cited by 26 publications

References 34 publications

µ-diff: A matlab toolbox for multiple scattering problems by disks

µ-diff: A matlab toolbox for multiple scattering problems by disks

Finite-difference simulations of transient radiation from a finite-length pipe

The DtN nonreflecting boundary condition for multiple scattering problems in the half-plane

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