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André Galligo - One of the best experts on this subject based on the ideXlab platform.

  • Constructing analysis-suitable parameterization of Computational Domain from CAD boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focus on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • constructing analysis suitable parameterization of Computational Domain from cad boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focuses on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • Optimal analysis-aware parameterization of Computational Domain in 3D isogeometric analysis
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis framework, Computational Domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various Computational Domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no self-intersections. In this paper, a linear and easy-to-check sufficient condition for injectivity of trivariate B-spline parameterization is proposed. By an example of 3D thermal conduction problem, we show that different parameterization of Computational Domain has different impact on the simulation result and efficiency in isogeometric analysis. For problems with exact solutions, we propose a shape optimization method to obtain optimal parameterization of Computational Domain. The proposed injective condition is used to check the injectivity of initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is the generalization of discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. Compared with the initial parameterization during refinement, the optimal parameterization can achieve the same accuracy but with less degrees of freedom.

  • Analysis-suitable volume parameterization of multi-block Computational Domain in isogeometric applications
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of multi-block Computational Domain in isogeometric version, i.e, how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parametrization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulted volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volume should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on three-dimensional heat conduction problem.

  • analysis suitable volume parameterization of multi block Computational Domain in isogeometric applications
    Computer-aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of the Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of the multi-block Computational Domain in an isogeometric version, i.e., how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of the single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parameterization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulting volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volumes should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on the three-dimensional heat conduction problem.

Bernard Mourrain - One of the best experts on this subject based on the ideXlab platform.

  • Constructing analysis-suitable parameterization of Computational Domain from CAD boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focus on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • constructing analysis suitable parameterization of Computational Domain from cad boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focuses on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • Optimal analysis-aware parameterization of Computational Domain in 3D isogeometric analysis
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis framework, Computational Domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various Computational Domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no self-intersections. In this paper, a linear and easy-to-check sufficient condition for injectivity of trivariate B-spline parameterization is proposed. By an example of 3D thermal conduction problem, we show that different parameterization of Computational Domain has different impact on the simulation result and efficiency in isogeometric analysis. For problems with exact solutions, we propose a shape optimization method to obtain optimal parameterization of Computational Domain. The proposed injective condition is used to check the injectivity of initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is the generalization of discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. Compared with the initial parameterization during refinement, the optimal parameterization can achieve the same accuracy but with less degrees of freedom.

  • Analysis-suitable volume parameterization of multi-block Computational Domain in isogeometric applications
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of multi-block Computational Domain in isogeometric version, i.e, how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parametrization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulted volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volume should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on three-dimensional heat conduction problem.

  • analysis suitable volume parameterization of multi block Computational Domain in isogeometric applications
    Computer-aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of the Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of the multi-block Computational Domain in an isogeometric version, i.e., how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of the single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parameterization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulting volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volumes should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on the three-dimensional heat conduction problem.

Detlef Lohse - One of the best experts on this subject based on the ideXlab platform.

  • effects of the Computational Domain size on direct numerical simulations of taylor couette turbulence with stationary outer cylinder
    Physics of Fluids, 2015
    Co-Authors: Rodolfo Ostillamonico, Roberto Verzicco, Detlef Lohse
    Abstract:

    In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the Computational Domain (“box”) size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to η = ri/ro = 0.909. The outer cylinder was kept stationary, while the inner rotated at a Reynolds number Rei = 105. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is found to play a minor role in the simulations, as the boxes are large enough. For all boxes studied, the spectra do not reach a box independent maximum.

  • Effects of the Computational Domain size on direct numerical simulations of Taylor-Couette turbulence with stationary outer cylinder
    Physics of Fluids, 2015
    Co-Authors: Rodolfo Ostilla Monico, Roberto Verzicco, Detlef Lohse
    Abstract:

    In search for the cheapest but still reliable numerical simulation, a systematic study on the effect of the Computational Domain ("box") size on direct numerical simulations of Taylor-Couette flow was performed. Four boxes, with varying azimuthal and axial extents were used. The radius ratio between the inner cylinder and the outer cylinder was fixed to $\eta=r_i/r_o=0.909$, and the outer was kept stationary, while the inner rotated at a Reynolds number $Re_i=10^5$. Profiles of mean and fluctuation velocities are compared, as well as autocorrelations and velocity spectra. The smallest box is found to accurately reproduce the torque and mean azimuthal velocity profiles of larger boxes, while having smaller values of the fluctuations than the larger boxes. The axial extent of the box directly reflects on the Taylor-rolls and plays a crucial role on the correlations and spectra. The azimuthal extent is also found to play a significant role, as larger boxes allow for azimuthal wave-like patterns in the Taylor rolls to develop, which affects the statistics in the bulk region. For all boxes studied, the spectra does not reach a box independent maximum.

Régis Duvigneau - One of the best experts on this subject based on the ideXlab platform.

  • Constructing analysis-suitable parameterization of Computational Domain from CAD boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focus on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • constructing analysis suitable parameterization of Computational Domain from cad boundary by variational harmonic method
    Journal of Computational Physics, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis, parameterization of Computational Domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the Computational Domain to parametric Domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of Computational Domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focuses on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal iso-parametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis.

  • Optimal analysis-aware parameterization of Computational Domain in 3D isogeometric analysis
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    In isogeometric analysis framework, Computational Domain is exactly described using the same representation as that employed in the CAD process. For a CAD object, we can construct various Computational Domain with same shape but with different parameterization. One basic requirement is that the resulting parameterization should have no self-intersections. In this paper, a linear and easy-to-check sufficient condition for injectivity of trivariate B-spline parameterization is proposed. By an example of 3D thermal conduction problem, we show that different parameterization of Computational Domain has different impact on the simulation result and efficiency in isogeometric analysis. For problems with exact solutions, we propose a shape optimization method to obtain optimal parameterization of Computational Domain. The proposed injective condition is used to check the injectivity of initial trivariate B-spline parameterization constructed by discrete Coons volume method, which is the generalization of discrete Coons patch method. Several examples and comparisons are presented to show the effectiveness of the proposed method. Compared with the initial parameterization during refinement, the optimal parameterization can achieve the same accuracy but with less degrees of freedom.

  • Analysis-suitable volume parameterization of multi-block Computational Domain in isogeometric applications
    Computer-Aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of multi-block Computational Domain in isogeometric version, i.e, how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parametrization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulted volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volume should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on three-dimensional heat conduction problem.

  • analysis suitable volume parameterization of multi block Computational Domain in isogeometric applications
    Computer-aided Design, 2013
    Co-Authors: Bernard Mourrain, Régis Duvigneau, André Galligo
    Abstract:

    Parameterization of the Computational Domain is a key step in isogeometric analysis just as mesh generation is in finite element analysis. In this paper, we study the volume parameterization problem of the multi-block Computational Domain in an isogeometric version, i.e., how to generate analysis-suitable parameterization of the multi-block Computational Domain bounded by B-spline surfaces. Firstly, we show how to find good volume parameterization of the single-block Computational Domain by solving a constraint optimization problem, in which the constraint condition is the injectivity sufficient conditions of B-spline volume parameterization, and the optimization term is the minimization of quadratic energy functions related to the first and second derivatives of B-spline volume parameterization. By using this method, the resulting volume parameterization has no self-intersections, and the isoparametric structure has good uniformity and orthogonality. Then we extend this method to the multi-block case, in which the continuity condition between the neighbor B-spline volumes should be added to the constraint term. The effectiveness of the proposed method is illustrated by several examples based on the three-dimensional heat conduction problem.

Constantine A. Balanis - One of the best experts on this subject based on the ideXlab platform.

  • Transparent Absorbing Boundary (TAB): In-Domain Computational Domain Truncation
    Applied Computational Electromagnetics, 2000
    Co-Authors: Jian Peng, Constantine A. Balanis
    Abstract:

    To truncate an unbounded space, a variety of techniques have been proposed [1–3]. Figure 1 shows a diagram of a traditional finite Computational Domain. Apparently, the presence of the transition Domain increases the Computational cost in the solution of the fields within the subject Domain. The popular Perfectly Matched Layer (PML) [4] provides a virtually reflection-free absorbing technique that makes it possible to reduce the thickness of the transition region. However, it still needs the additional Domain to absorb the outward traveling waves.

  • A generalized reflection-free Domain-truncation method: transparent absorbing boundary
    IEEE Transactions on Antennas and Propagation, 1998
    Co-Authors: Jian Peng, Constantine A. Balanis
    Abstract:

    A generalized technique is developed to truncate the Computational Domain without reflection. It transforms the unbounded-space Maxwell's equations to a set of auxiliary equations in a closed Domain. A reflection-free amplitude-reduction scheme applied over the entire Computational Domain reduces the auxiliary field components outwardly and makes them equal to zero at the closed boundary. No additional absorbing region surrounding the Domain of interest is needed with this technique because the relationship between the physical fields and their auxiliary counterparts is explicitly known and the former can be found from the latter within the Computational Domain.

  • Transparent absorbing boundary (TAB) for the truncation of the Computational Domain
    IEEE Microwave and Guided Wave Letters, 1997
    Co-Authors: Jian Peng, Constantine A. Balanis
    Abstract:

    A new approach to Domain truncation without reflection is proposed for finite methods. The open-space Maxwell's equations, along with boundary conditions, are transformed to an equivalent system with a homogeneous closed boundary; the latter is then solved numerically. Like the popular perfectly matched layer (PML), the new method is independent of frequency and incident angle. Its uniqueness is that it does not need the extra absorption region, since the field attenuation takes place in the Domain of the subject.