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Charbel Farhat - One of the best experts on this subject based on the ideXlab platform.

  • a hybrid discontinuous in space and time galerkin method for Wave propagation problems
    International Journal for Numerical Methods in Engineering, 2014
    Co-Authors: Dalei Wang, Radek Tezaur, Charbel Farhat
    Abstract:

    SUMMARY Medium-frequency regime and multi-scale Wave propagation problems have been a subject of active research in computational acoustics recently. New techniques have attempted to overcome the limitations of existing discretization methods that tend to suffer from dispersion. One such technique, the discontinuous enrichment method, incorporates features of the governing partial differential Equation in the approximation, in particular, the solutions of the Homogeneous form of the Equation. Here, based on this concept and by extension of a conventional space–time finite element method, a hybrid discontinuous Galerkin method (DGM) for the numerical solution of transient problems governed by the Wave Equation in two and three spatial dimensions is described. The discontinuous formulation in both space and time enables the use of solutions to the Homogeneous Wave Equation in the approximation. In this contribution, within each finite element, the solutions in the form of polynomial Waves are employed. The continuity of these polynomial Waves is weakly enforced through suitably chosen Lagrange multipliers. Results for two-dimensional and three-dimensional problems, in both low-frequency and medium-frequency regimes, show that the proposed DGM outperforms the conventional space–time finite element method. Copyright © 2014 John Wiley & Sons, Ltd.

  • a space time discontinuous galerkin method for the solution of the Wave Equation in the time domain
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: Steffen Petersen, Charbel Farhat, Radek Tezaur
    Abstract:

    In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale Wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential Equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the Wave Equation. We present a space–time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the Homogeneous Wave Equation. The use of hierarchical Wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space–time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd.

Radek Tezaur - One of the best experts on this subject based on the ideXlab platform.

  • a hybrid discontinuous in space and time galerkin method for Wave propagation problems
    International Journal for Numerical Methods in Engineering, 2014
    Co-Authors: Dalei Wang, Radek Tezaur, Charbel Farhat
    Abstract:

    SUMMARY Medium-frequency regime and multi-scale Wave propagation problems have been a subject of active research in computational acoustics recently. New techniques have attempted to overcome the limitations of existing discretization methods that tend to suffer from dispersion. One such technique, the discontinuous enrichment method, incorporates features of the governing partial differential Equation in the approximation, in particular, the solutions of the Homogeneous form of the Equation. Here, based on this concept and by extension of a conventional space–time finite element method, a hybrid discontinuous Galerkin method (DGM) for the numerical solution of transient problems governed by the Wave Equation in two and three spatial dimensions is described. The discontinuous formulation in both space and time enables the use of solutions to the Homogeneous Wave Equation in the approximation. In this contribution, within each finite element, the solutions in the form of polynomial Waves are employed. The continuity of these polynomial Waves is weakly enforced through suitably chosen Lagrange multipliers. Results for two-dimensional and three-dimensional problems, in both low-frequency and medium-frequency regimes, show that the proposed DGM outperforms the conventional space–time finite element method. Copyright © 2014 John Wiley & Sons, Ltd.

  • a space time discontinuous galerkin method for the solution of the Wave Equation in the time domain
    International Journal for Numerical Methods in Engineering, 2009
    Co-Authors: Steffen Petersen, Charbel Farhat, Radek Tezaur
    Abstract:

    In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale Wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential Equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the Wave Equation. We present a space–time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the Homogeneous Wave Equation. The use of hierarchical Wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space–time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd.

Andrew Y. T. Leung - One of the best experts on this subject based on the ideXlab platform.

  • The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity
    Nonlinear Dynamics, 2011
    Co-Authors: Yiu-yin Lee, Andrew Y. T. Leung
    Abstract:

    Theoretical analysis of the nonlinear vibration effects on the sound absorption of a panel absorber and sound transmission loss of a panel backed by a rectangular cavity is herein presented. The harmonic balance method is employed to derive a structural acoustic formulation from two-coupled partial differential Equations representing the nonlinear structural forced vibration and induced acoustic pressure; one is the well-known von Karman’s plate Equation and the other is the Homogeneous Wave Equation. This method has been used in a previous study of nonlinear structural vibration, in which its results agreed well with the elliptic solution. To date, very few classical solutions for this nonlinear structural-acoustic problem have been developed, although there are many for nonlinear plate or linear structural-acoustic problems. Thus, for verification purposes, an approach based on the numerical integration method is also developed to solve the nonlinear structural-acoustic problem. The solutions obtained with the two methods agree well with each other. In the parametric study, the panel displacement amplitude converges with increases in the number of harmonic terms and acoustic and structural modes. The effects of excitation level, cavity depth, boundary condition, and damping factor are also examined. The main findings include the following: (1) the well-known “jump phenomenon” in nonlinear vibration is seen in the sound absorption and transmission loss curves; (2) the absorption peak and transmission loss dip due to the nonlinear resonance are significantly wider than those in the linear case because of the wider resonant bandwidth; and (3) nonlinear vibration has the positive effect of widening the absorption bandwidth, but it also degrades the transmission loss at the resonant frequency.

Bradley E Treeby - One of the best experts on this subject based on the ideXlab platform.

  • a k space green s function solution for acoustic initial value problems in Homogeneous media with power law absorption
    Journal of the Acoustical Society of America, 2011
    Co-Authors: Bradley E Treeby, Ben Cox
    Abstract:

    An efficient Green’s function solution for acoustic initial value problems in Homogeneous media with power law absorption is derived. The solution is based on the Homogeneous Wave Equation for lossless media with two additional terms. These terms are dependent on the fractional Laplacian and separately account for power law absorption and dispersion. Given initial conditions for the pressure and its temporal derivative, the solution allows the pressure field for any time t>0 to be calculated in a single step using the Fourier transform and an exact k-space time propagator. For regularly spaced Cartesian grids, the former can be computed efficiently using the fast Fourier transform. Because no time stepping is required, the solution facilitates the efficient computation of the pressure field in one, two, or three dimensions without stability constraints. Several computational aspects of the solution are discussed, including the effect of using a truncated Fourier series to represent discrete initial condit...

  • a k space green s function solution for acoustic initial value problems in Homogeneous media with power law absorption
    Journal of the Acoustical Society of America, 2011
    Co-Authors: Bradley E Treeby, B T Cox
    Abstract:

    An efficient Green’s function solution for acoustic initial value problems in Homogeneous media with power law absorption is derived. The solution is based on the Homogeneous Wave Equation for lossless media with two additional terms. These terms are dependent on the fractional Laplacian and separately account for power law absorption and dispersion. Given initial conditions for the pressure and its temporal derivative, the solution allows the pressure field for any time t>0 to be calculated in a single step using the Fourier transform and an exact k-space time propagator. For regularly spaced Cartesian grids, the former can be computed efficiently using the fast Fourier transform. Because no time stepping is required, the solution facilitates the efficient computation of the pressure field in one, two, or three dimensions without stability constraints. Several computational aspects of the solution are discussed, including the effect of using a truncated Fourier series to represent discrete initial conditions, the use of smoothing, and the properties of the encapsulated absorption and dispersion.

Rodney J Sobey - One of the best experts on this subject based on the ideXlab platform.