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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.
A Taxonomy of consistently stabilized finite element methods for the Stokes problem
 SIAM J. Sci. Comp
"... Abstract. Stabilized mixed methods can circumvent the restrictive infsup condition without introducing penalty errors. For properly chosen stabilization parameters these methods are wellposed for all conforming velocitypressure pairs. However, their variational forms have widely varying properties ..."
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Cited by 23 (7 self)
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Abstract. Stabilized mixed methods can circumvent the restrictive infsup condition without introducing penalty errors. For properly chosen stabilization parameters these methods are wellposed for all conforming velocitypressure pairs. However, their variational forms have widely varying properties. First, stabilization offers a choice between weakly or strongly coercive bilinear forms that give rise to linear systems with identical solutions but very different matrix properties. Second, coercivity may be conditional upon a proper choice of a stabilizing parameter. Here we focus on how these two aspects of stabilized methods affect their accuracy and efficient iterative solution. We present results that indicate a preference of Krylov subspace solvers for strongly coercive formulations. Stability criteria obtained by finite element and algebraic analyses are compared with numerical experiments. While for two popular classes of stabilized methods, sufficient stability bounds correlate well with numerical stability, our experiments indicate the intriguing possibility that the pressurestabilized Galerkin method is unconditionally stable.
Complex wavenumber Fourieranalysis of the pversion finite element method
 Computational Mechanics
, 1995
"... Highorder nite element discretizations of the reduced wave equation have frequency bands where the solutions are harmonic decaying waves. In these so called ‘stopping ’ bands, the solutions are not purely propagating (real wavenumbers) but are attenuated (complex wavenumbers). In this paper we ext ..."
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Cited by 23 (5 self)
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Highorder nite element discretizations of the reduced wave equation have frequency bands where the solutions are harmonic decaying waves. In these so called ‘stopping ’ bands, the solutions are not purely propagating (real wavenumbers) but are attenuated (complex wavenumbers). In this paper we extend the standard dispersion analysis technique to include complex wavenumbers. We then use this complex Fourier analysis technique to examine the dispersion and attenuation characteristics of the p{version nite element method. Practical guidelines are reported for phase and amplitude accuracy in terms of the spectral order and the number of elements per wavelength.
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
Design of Galerkin Generalized Least Squares Methods for Timoshenko Beams
, 1996
"... A class of finite element methods, the Galerkin Generalized Least Squares methods, are developed and applied to model the steadystate response of Timoshenko beams. An optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error. Th ..."
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Cited by 7 (2 self)
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A class of finite element methods, the Galerkin Generalized Least Squares methods, are developed and applied to model the steadystate response of Timoshenko beams. An optimal method is designed using a linear interpolation of the response such that there is zero finite element dispersion error. The classical method of selective reduced integration and a modified version of selective reduced integration with mass lumping are shown to fall under the Galerkin Generalized Least Squares framework. Numerical experiments in wave propagation demonstrate the dramatic superiority of the new optimal method over the standard approaches. The goal of the new methods is to decrease the computational burden required to achieve a desired accuracy level at a particular frequency thereby enabling larger scale, higher frequency computations for a given platform. 1. Introduction In this paper, Galerkin and Galerkin Generalized Least Squares finite element methods for the steadystate vibration of Timos...
Advances in SpaceTime Finite Element Methods for Structural Acoustics and FluidSolid Interaction
"... Traditional computational approaches toward simulation of radiation and scattering from elastic bodies submerged in an acoustic fluid have been primarily based on frequency domain formulations. Classical timeharmonic approaches (including boundary element, finite element, and finite difference meth ..."
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Cited by 1 (1 self)
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Traditional computational approaches toward simulation of radiation and scattering from elastic bodies submerged in an acoustic fluid have been primarily based on frequency domain formulations. Classical timeharmonic approaches (including boundary element, finite element, and finite difference methods) have been effective for problems involving a limited number of frequencies (narrow band response) and scales (wavelengths) that are large compared to the characteristic dimensions of the elastic structure. Attempts at solving largescale structural acoustic systems with dimensions that are much larger than the operating wavelengths and which are complex, consisting of many different components with different scales and broadband frequencies, has revealed limitations of many of the classical methods. As a result, in recent times there has been renewed interest in new and alternative approaches, including timedomain approaches. This paper describes recent advances in the development of a...
Implementation Of NonReflecting Boundaries In A SpaceTime Finite Element Method For Structural Acoustics
, 1997
"... This paper examines the development and implementation of secondorder accurate nonreflecting boundary conditions in a timediscontinuous Galerkin finite element method for structural acoustics in unbounded domains. The formulation is based on a multifield spacetime variational equation for both ..."
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This paper examines the development and implementation of secondorder accurate nonreflecting boundary conditions in a timediscontinuous Galerkin finite element method for structural acoustics in unbounded domains. The formulation is based on a multifield spacetime variational equation for both the acoustic fluid and elastic solid together with their interaction. This approach to the modeling of the temporal variables allows for the consistent use of highorder accurate adaptive solution strategies for unstructured finite elements in both time and space. An important feature of the method is the incorporation of temporal jump operators which allow for discretizations that are discontinuous in time. Two alternative approaches are examined for implementing nonreflecting boundaries within a timediscontinuous Galerkin finite element method; direct implementation of the exterior acoustic impedance through a weighted variational equation in time and space, and indirectly through a decom...
unknown title
, 2008
"... Performance assessment of a new class of local absorbing boundary conditions for ellipticaland prolate spheroidalshaped boundaries ..."
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Performance assessment of a new class of local absorbing boundary conditions for ellipticaland prolate spheroidalshaped boundaries