scholarly journals ANALYTIC PRECONDITIONERS FOR THE BOUNDARY INTEGRAL SOLUTION OF THE SCATTERING OF ACOUSTIC WAVES BY OPEN SURFACES

2005 ◽  
Vol 13 (03) ◽  
pp. 477-498 ◽  
Author(s):  
XAVIER ANTOINE ◽  
ABDERRAHMANE BENDALI ◽  
MARION DARBAS
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integral Solution ◽  
Open Surface ◽  
Efficient Tool ◽  
Closed Surfaces ◽  
Scattering Of Acoustic Waves

This study is devoted to some numerical issues in the boundary integral solution of the scattering of an acoustic wave by an open surface. More precisely, it deals with the construction of a cheap analytical preconditioner to enhance the iterative solving of this kind of equation. Detailed attention is paid to bring out the reasons that make this construction much more difficult than for closed surfaces. This preconditioner is carefully tested and compared to two more usual ones for two and three dimensional problems. It is shown that this preconditioner provides a cheap and efficient tool making reliable the iterative solving. The discussion also precisely brings out the issues where further studies are still needed to improve its efficiency.

scholarly journals Identification of an unbounded bi-periodic interface for the inverse fluid-solid interaction problem

2021 ◽  
Author(s):  
Yanli Cui ◽  
Fenglong Qu ◽  
Changkun Wei
Keyword(s):  
Acoustic Waves ◽  
Near Field ◽  
A Priori ◽  
Scattering Problem ◽  
Three Dimensional ◽  
A Priori Estimate ◽  
Countably Infinite ◽  
Fluid Solid Interaction ◽  
Interaction Problem ◽  
Scattering Of Acoustic Waves

This paper is concerned with the inverse scattering of acoustic waves by an unbounded periodic elastic medium in the three-dimensional case. A novel uniqueness theorem is proved for the inverse problem of recovering a bi-periodic interface between acoustic and elastic waves using the near-field data measured only from the acoustic side of the interface, corresponding to a countably infinite number of quasi-periodic incident acoustic waves. The proposed method depends only on a fundamental a priori estimate established for the acoustic and elastic wave fields and a new mixed-reciprocity relation established in this paper for the solutions of the fluid-solid interaction scattering problem.

scholarly journals A General Algorithm for the Numerical Solution of Hypersingular Boundary Integral Equations

1992 ◽  
Vol 59 (3) ◽  
pp. 604-614 ◽  
Author(s):  
M. Guiggiani ◽  
G. Krishnasamy ◽  
T. J. Rudolphi ◽  
F. J. Rizzo
Keyword(s):  
Integral Equations ◽  
Boundary Integral Equations ◽  
Collocation Point ◽  
Three Dimensional ◽  
Careful Analysis ◽  
Boundary Integral ◽  
Hypersingular Integrals ◽  
Closed Surfaces ◽  
First Time ◽  
General Method

The limiting process that leads to the formulation of hypersingular boundary integral equations is first discussed in detail. It is shown that boundary integral equations with hypersingular kernels are perfectly meaningful even at non-smooth boundary points, and that special interpretations of the integrals involved are not necessary. Careful analysis of the limiting process has also strong relevance for the development of an appropriate numerical algorithm. In the second part, a new general method for the evaluation of hypersingular surface integrals in the boundary element method (BEM) is presented. The proposed method can be systematically applied in any BEM analysis, either with open or closed surfaces, and with curved boundary elements of any kind and order (of course, provided the density function meets necessary regularity requirements at each collocation point). The algorithm operates in the parameter plane of intrinsic coordinates and allows any hypersingular integral in the BEM to be directly transformed into a sum of a double and a one-dimensional regular integrals. Since all singular integrations are performed analytically, standard quadrature formulae can be used. For the first time, numerical results are presented for hypersingular integrals on curved (distorted) elements for three-dimensional problems.

scholarly journals Three-dimensional acoustic scattering by layered media: a novel surface formulation with operator expansions implementation

2011 ◽  
Vol 468 (2139) ◽  
pp. 731-758 ◽  
Author(s):  
David P. Nicholls
Keyword(s):  
Acoustic Waves ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Boundary Integral ◽  
Helmholtz Equations ◽  
Irregular Structures ◽  
Wide Range ◽  
Order Of Magnitude ◽  
Boundary Integral Operators ◽  
Operator Expansions

The scattering of acoustic waves by irregular structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses on the rapid and highly accurate numerical approximation of solutions of Helmholtz equations coupled across irregular periodic interfaces meant to model acoustic waves incident upon a multi-layered medium. We describe not only a novel surface formulation for the problem in terms of boundary integral operators (Dirichlet–Neumann operators), but also a Boundary Perturbation methodology (the Method of Operator Expansions) for its numerical simulation. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than volumetric approaches), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Malcolm & Nicholls' Operator Expansions algorithm for dielectric structures with two layers. As with this precursor, this approach is efficient and spectrally accurate.

Cavitation Bubble in Compressible Fluid Near the Rigid Wall Subjected to the Acoustic Wave with Arbitrary Incidence Angle in Three-Dimensional

2014 ◽  
Vol 31 (3) ◽  
pp. 307-318 ◽  
Author(s):  
X. Ye ◽  
X.-L. Yao ◽  
L.-Q. Sun ◽  
B. Wang
Keyword(s):  
Acoustic Wave ◽  
Cavitation Bubble ◽  
High Speed ◽  
Incidence Angle ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Sound Field ◽  
Rigid Wall ◽  
Boundary Integral ◽  
Three Dimensional Model

AbstractA balanced cavitation bubble is released near the rigid wall in the sound field generated by the incidence plane wave and its reflecting wave. With the modified boundary integral equation, the dynamics of bubble is solved considering the compressibility of fluid in this paper. Also the Bernoulli equation as the boundary condition for cavitation bubble in sound field is deduced using Euler equation. Since the arbitrary incidence angle of acoustic wave, the three-dimensional model is utilized. The bubble will expand or contract at first according to the initial phase of acting acoustic pressure on bubble surface. And during the contraction phase, the liquid jet with high speed will be generated pointing to rigid wall but be deflected to the incidence direction of acoustic wave. The oblique degree of jet will be affected by the incidence angle and initial distance between bubble center and rigid wall. The oscillation amplitude of bubble will be affected by the incidence amplitude and incidence frequency, but be limited by the rigid wall. Since the compressibility of fluid, the perturbation will propagate to the far-field. Thus the oscillation amplitude of bubble will be reduced.

scholarly journals The Experimental Registration of the Evanescent Acoustic Wave in YX LiNbO3 Plate

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2238
Author(s):  
Andrey Smirnov ◽  
Boris Zaitsev ◽  
Andrey Teplykh ◽  
Ilya Nedospasov ◽  
Egor Golovanov ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Evanescent Waves ◽  
Electrical Boundary Conditions ◽  
3D Finite Element Method ◽  
First Time ◽  
Theoretical Results ◽  
Good Agreement ◽  
Piezoelectric Plates

Evanescent acoustic waves are characterized by purely imaginary or complex wavenumbers. Earlier, in 2019 by using a three dimensional (3D) finite element method (FEM) the possibility of the excitation and registration of such waves in the piezoelectric plates was theoretically shown. In this paper the set of the acoustically isolated interdigital transducers (IDTs) with the different spatial periods for excitation and registration of the evanescent acoustic wave in Y-cut X-propagation direction of lithium niobate (LiNbO3) plate was specifically calculated and produced. As a result, the possibility to excite and register the evanescent acoustic wave in the piezoelectric plates was experimentally proved for the first time. The evanescent nature of the registered wave has been established. The theoretical results turned out to be in a good agreement with the experimental ones. The influence of an infinitely thin layer with arbitrary conductivity placed on a plate surface was also investigated. It has been shown that the frequency region of an evanescent acoustic wave existence is very sensitive to the changes of the electrical boundary conditions. The results obtained may be used for the development of the method of the analysis of thin films electric properties based on the study of evanescent waves.

Numerical solution of integral equations for the three-dimensional scalar diffraction problems

2018 ◽  
Author(s):  
С.И. Смагин ◽  
А.А. Каширин
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Acoustic Waves ◽  
Boundary Integral Equations ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Special Method ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Wide Range

Рассматриваются задачи дифракции (трансмиссии) стационарных акустических волн на трехмерных однородных включениях. Методами теории потенциала для них получены два слабо сингулярных граничных интегральных уравнения Фредгольма первого рода с одной неизвестной функцией, каждое из которых эквивалентно исходной задаче. Интегральные уравнения аппроксимируются системами линейных алгебраических уравнений, которые затем решаются численно итерационным методом обобщенных минимальных невязок GMRES. При дискретизации этих уравнений используется специальный метод осреднения интегральных операторов со слабыми особенностями в ядрах, позволяющий получать системы с легко вычисляемыми коэффициентами. Метод допускает эффективное распараллеливание и позволяет проводить расчеты в широком диапазоне волновых чисел. Приводятся результаты вычислительных экспериментов, позволяющие судить о возможностях предлагаемого подхода. Purpose. The purpose of the article is to develop efficient algorithms for numerical solution of the diffraction (transmission) problem of stationary acoustic waves on threedimensional homogeneous inclusions. Methods. By using the combinations of simple and double layer potentials, two Fredholm boundary integral equations of the first kind with one unknown function are obtained for these potentials, each of which is equivalent to the original problem. When sampling these equations, a special method of averaging integral operators with weak singularities in the kernels is applied. Outcomes. The obtained integral equations are approximated by systems of linear algebraic equations with easily-calculated coefficients, which are then solved numerically by means of the generalized method of minimal residuals (GMRES). A series of computing experiments for numerical solution of particular stationary three-dimensional diffraction problems of acoustic waves has been conducted. Conclusions. Computing experiments have shown that the proposed numerical method possesses high accuracy in finding approximate solutions of these problems. It allows both effective parallelization and ability to perform calculations in a wide range of wave numbers and can be used to solve other problems of mathematical physics, formulated in the form of boundary integral equations.

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