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15
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 219 (4 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Recent Developments in Finite Element Methods for Structural Acoustics
, 1996
"... This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics ..."
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Cited by 14 (3 self)
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This paper reviews recent progress in finite element analysis that renders computation a practical tool for solving problems of structural acoustics
A weakly singular form of the hypersingular boundary integral equation applied to 3D acoustic wave problems
, 1992
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Adaptive boundary element method of timeharmonic exterior acoustic problems in two dimensions
 Comput. Methods Appl. Mech. Engrg
"... In this paper we carry out boundary element computations of the Helmholtz equation in two dimensions, in the context of timeharmonic exterior acoustics. The purpose is to demonstrate cost savings engendered through adaptivity for propagating solutions at moderate wave numbers. The computation are p ..."
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Cited by 7 (3 self)
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In this paper we carry out boundary element computations of the Helmholtz equation in two dimensions, in the context of timeharmonic exterior acoustics. The purpose is to demonstrate cost savings engendered through adaptivity for propagating solutions at moderate wave numbers. The computation are performed on meshes of constant boundary elements, and are adapted to the solution by locally changing element sizes (hversion). Burton and Miller approach is employed to solve the exterior problems for all wave numbers. Two error indicators obtained from the dual integral equations in conjunction with the exact error indicator are used for local error estimation, which are essential ingredients for all adaptive mesh schemes in BEM. Computational experiments are performed for the twodimensional exterior acoustics. The three error tracking curves are in good agreement with their shapes. Three examples show that the adaptive mesh based on the error indicators converge to the exact solution more efficiently using the same number of elements than does uniform mesh discretization. 2002 Elsevier Science B.V. All rights reserved.
Fast Numerical Methods for High Frequency Wave Scattering
, 2012
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Multiscale Finite Elements for Acoustics: Continuous, Discontinuous, and Stabilized Methods
 INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING, 6(5&6)
, 2008
"... This work describes two perspectives for understanding the numerical difficulties that arise in the solution of wave problems, and various advances in the development of efficient discretization schemes for acoustics. Standard, loworder, continuous Galerkin finite element methods are unable to cop ..."
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Cited by 1 (0 self)
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This work describes two perspectives for understanding the numerical difficulties that arise in the solution of wave problems, and various advances in the development of efficient discretization schemes for acoustics. Standard, loworder, continuous Galerkin finite element methods are unable to cope with wave phenomena at short wave lengths because the computational effort required to resolve the waves and control numerical dispersion errors becomes prohibitive. The failure to adequately represent subgrid scales misses not only the finescale part of the solution, but often causes severe pollution of the solution on the resolved scale as well. Since computation naturally separates the scales of a problem according to the mesh size, multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them. The Galerkin/least squares method arises in multiscale settings, and its stability parameter is defined by dispersion considerations. Bubble enriched methods employ auxiliary functions that are usually expressed in the form of infinite series. Dispersion analysis provides guidelines for the implementation of the series representation in practice. In the discontinuous enrichment method, the fine scales are spanned by freespace homogeneous solutions of the governing equations. These auxiliary functions may be discontinuous across element boundaries, and continuity is enforced weakly by Lagrange multipliers.
A FullWave Helmholtz Model for ContinuousWave Ultrasound Transmission
"... A fullwave Helmholtz model of continuouswave (CW) ultrasound fields may offer several attractive features over widely used partialwave approximations. For example, many fullwave techniques can be easily adjusted for complex geometries and multiple reflections of sound are automatically taken int ..."
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A fullwave Helmholtz model of continuouswave (CW) ultrasound fields may offer several attractive features over widely used partialwave approximations. For example, many fullwave techniques can be easily adjusted for complex geometries and multiple reflections of sound are automatically taken into account in the model. To date, however, the fullwave modeling of CW fields in general 3D geometries has been avoided due to large computational cost associated with the numerical approximation of the Helmholtz equation. Recent developments in computing capacity together with improvements in finite element type modeling techniques are making possible wave simulations in 3D geometries which reach over tens of wavelengths. The aim of this study is to investigate the feasibility of a fullwave solution of the 3D Helmholtz equation for modeling of continuouswave ultrasound fields in an inhomogeneous medium. The numerical approximation of the Helmholtz equation is computed using the ultra weak variational formulation (UWVF) method. In addition, an inverse problem technique is utilized to reconstruct the velocity distribution on the transducer which is used to model the sound source in the UWVF scheme. The modeling method is verified by comparing simulated and measured fields in the case of transmission of 531 kHz CW fields through layered plastic plates. The comparison shows a reasonable agreement between simulations and measurements at low angles of incidence but due to mode conversion, the Helmholtz model becomes insufficient for simulating ultrasound fields in plates at large angles of incidence. I.
Computational methods for multiple scattering at high frequency with applications to periodic structure calculations
 IN "WAVE PROPAGATION IN PERIODIC MEDIA. ANALYSIS, NUMERICAL TECHNIQUES AND PRACTICAL APPLICATIONS", M. EHRHARDT (EDITOR), PROGRESS IN COMPUTATIONAL PHYSICS (PICP
, 2010
"... The aim of this paper is to explain some recent numerical methods for solving highfrequency scattering problems. Most particularly, we focus on the multiple scattering problem where rays are multiply bounced by a collection of separate objects. We review recent developments for three main familie ..."
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The aim of this paper is to explain some recent numerical methods for solving highfrequency scattering problems. Most particularly, we focus on the multiple scattering problem where rays are multiply bounced by a collection of separate objects. We review recent developments for three main families of approaches: Fourier series based methods, Partial Differential Equations approaches and Integral Equations based techniques. Furthermore, for each of these three families of methods, we present original procedures for solving the highfrequency multiple scattering problem. Computational examples are given, in particular for finite periodic structures calculations. Difficulties for solving such problems are explained, showing that many serious simulation problems are still open.