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W A Johnson - One of the best experts on this subject based on the ideXlab platform.

  • 6 d mom reaction integrals evaluated via the Divergence Theorem
    International Conference on Electromagnetics in Advanced Applications, 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this contribution we propose an accurate and efficient numerical evaluation of 6-D reaction integrals that appear in the Method of Moment (MoM) discretization of Volume Integral Equations (VIEs).

  • Evaluation of 6-D MoM Integrals by Application of the Divergence Theorem with Singularity Subtraction Acceleration
    2021 15th European Conference on Antennas and Propagation (EuCAP), 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    We propose to evaluate the double-volumetric integrals appearing in MoM formulations for volumetric integral equations by applying the Divergence Theorem to reduce both source and test integrals to surface integrals. Their integrands consist of the original kernel, basis, and test functions integrated twice radially in closed form. Implementing the surface integrals directly in the physical domain eliminates the restrictions to well-shaped elements. For faceted volumetric elements, the surface integrals reduce to the evaluation of interaction integrals between source and test face pairs. Triangular facets may be either integrated directly in barycentric coordinates or in a cylindrical coordinate system whose axis is the line of intersection of planes containing source and test face pairs. Further smoothing of the integrand is provided by first removing the static asymptotic form of the integrand from the integral, then restoring its contribution as a closed form integral whose removal accelerates convergence of the difference integral.

  • reducing the dimensionality of 6 d mom integrals applying twice the Divergence Theorem
    European Conference on Antennas and Propagation, 2020
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this paper we propose a scheme for evaluating the 6-D interaction integrals appearing in volume integral equation solved with the Method of Moments and tetrahedral elements. We treat as a whole the double volume integral, applying the Divergence Theorem first on the source domain and then on the test domain. With the proper variable transformation and reordering, the 6-D integrals are expressed as two radial integrals plus four linear integrals over the source and observation domain planes.

  • acceleration of volume volume 6 d integrals for numerical evaluation by double application of the Divergence Theorem
    2019 International Applied Computational Electromagnetics Society Symposium (ACES), 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In the present paper, we propose the application of the surface Divergence Theorem for the integration of double volumetric integrals for both source and test domain of the 6-D reaction integrals. The resulting 6-D volume integrals are expressed as two radial integrals plus two surface integrals over the source and observation domain boundaries. The radial integrations in the physical domain should be well-behaved and easily performed for arbitrary polyhedral domains. The method is numerically validated for static and dynamic kernels arising in the Electric Field Integral Equation (EFIE), i.e., for kernels with 1/R singularities, and linear basis functions.

  • evaluation of 4 d reaction integrals via double application of the Divergence Theorem
    IEEE Transactions on Antennas and Propagation, 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    The use of the method of moments to solve surface integral equations is one of the most popular numerical techniques in electromagnetic modeling and analysis. This method requires the accurate and efficient numerical evaluation of iterated surface integrals over both source and testing domains. In this paper, we propose a scheme for evaluating these 4-D interaction integrals between pairs of arbitrarily positioned and oriented elements. The approach is based on applying the surface Divergence Theorem twice, once on the source and once on the test domain. When the integrations are reordered as two outer contour integrals plus two inner radial integrals, the initial radial integrations provide significant smoothing of the underlying singular integrands. The method is numerically validated for static and dynamic kernels arising in the electric field integral equation, i.e., for kernels with $1/R$ singularities, and linear basis functions. The proposed formula to evaluate 4-D reaction integrals can be extended to different kernels and to different elements, e.g., to curved or volumetric elements, and to basis functions of higher order.

Detao Wan - One of the best experts on this subject based on the ideXlab platform.

  • a linear smoothed quadratic finite element for the analysis of laminated composite reissner mindlin plates
    Composite Structures, 2017
    Co-Authors: Detao Wan, Sundararajan Natarajan, Stéphane Bordas, Ting Long
    Abstract:

    Abstract It is well known that the high-order elements have significantly improved the accuracy of solutions in the traditional finite element analysis, but the performance of high-order elements is restricted by the shear-locking and distorted meshes for the plate problems. In this paper, a linear smoothed eight-node Reissner-Mindlin plate element (Q8 plate element) based on the first order shear deformation theory is developed for the static and free vibration analysis of laminated composite plates, the computation of the interior derivatives of shape function and isoparametric mapping can be removed. The strain matrices are modified with a linear smoothing technique by using the Divergence Theorem between the nodal shape functions and their derivatives in Taylor’s expansion. Moreover, the first order Taylor’s expansion is also employed for the construction of stiffness matrix to satisfy the linear strain distribution. Several numerical examples indicate that the novel Q8 plate element has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes.

  • A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities
    International Journal for Numerical Methods in Engineering, 2016
    Co-Authors: Detao Wan, Sundararajan Natarajan, Stéphane Bordas, Gang Yang
    Abstract:

    In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian Divergence Theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion.

  • a novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis
    Meccanica, 2016
    Co-Authors: Gang Yang, Detao Wan
    Abstract:

    The solution of mass matrix is one of the important parts for dynamic analysis of finite element method (FEM). In general FEM procedure, the numerical integration of consistent mass matrix needs to carry out the same operation as the stiffness matrix, which includes the coordinate mapping and computing of Jacobian matrix. There has been proposed smoothed finite element method for evaluating stiffness matrix to avoid the coordinate mapping and computing of Jacobian matrix in the numerical integration. In this work, a novel integration scheme is proposed to calculate the consistent mass matrix, in which a symbolic integration is implemented by combining indefinite integral with Gauss Divergence Theorem. Then, the novel integration scheme of consistent mass matrix is incorporated with the smoothing strain technique for free and forced vibration analysis. The accuracy and the convergence properties of the present method are investigated by several numerical examples. It can be concluded from the numerical results that the present method is robust and stability for dynamic analysis.

D R Wilton - One of the best experts on this subject based on the ideXlab platform.

  • 6 d mom reaction integrals evaluated via the Divergence Theorem
    International Conference on Electromagnetics in Advanced Applications, 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this contribution we propose an accurate and efficient numerical evaluation of 6-D reaction integrals that appear in the Method of Moment (MoM) discretization of Volume Integral Equations (VIEs).

  • Evaluation of 6-D MoM Integrals by Application of the Divergence Theorem with Singularity Subtraction Acceleration
    2021 15th European Conference on Antennas and Propagation (EuCAP), 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    We propose to evaluate the double-volumetric integrals appearing in MoM formulations for volumetric integral equations by applying the Divergence Theorem to reduce both source and test integrals to surface integrals. Their integrands consist of the original kernel, basis, and test functions integrated twice radially in closed form. Implementing the surface integrals directly in the physical domain eliminates the restrictions to well-shaped elements. For faceted volumetric elements, the surface integrals reduce to the evaluation of interaction integrals between source and test face pairs. Triangular facets may be either integrated directly in barycentric coordinates or in a cylindrical coordinate system whose axis is the line of intersection of planes containing source and test face pairs. Further smoothing of the integrand is provided by first removing the static asymptotic form of the integrand from the integral, then restoring its contribution as a closed form integral whose removal accelerates convergence of the difference integral.

  • reducing the dimensionality of 6 d mom integrals applying twice the Divergence Theorem
    European Conference on Antennas and Propagation, 2020
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this paper we propose a scheme for evaluating the 6-D interaction integrals appearing in volume integral equation solved with the Method of Moments and tetrahedral elements. We treat as a whole the double volume integral, applying the Divergence Theorem first on the source domain and then on the test domain. With the proper variable transformation and reordering, the 6-D integrals are expressed as two radial integrals plus four linear integrals over the source and observation domain planes.

  • acceleration of volume volume 6 d integrals for numerical evaluation by double application of the Divergence Theorem
    2019 International Applied Computational Electromagnetics Society Symposium (ACES), 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In the present paper, we propose the application of the surface Divergence Theorem for the integration of double volumetric integrals for both source and test domain of the 6-D reaction integrals. The resulting 6-D volume integrals are expressed as two radial integrals plus two surface integrals over the source and observation domain boundaries. The radial integrations in the physical domain should be well-behaved and easily performed for arbitrary polyhedral domains. The method is numerically validated for static and dynamic kernels arising in the Electric Field Integral Equation (EFIE), i.e., for kernels with 1/R singularities, and linear basis functions.

  • evaluation of 4 d reaction integrals via double application of the Divergence Theorem
    IEEE Transactions on Antennas and Propagation, 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    The use of the method of moments to solve surface integral equations is one of the most popular numerical techniques in electromagnetic modeling and analysis. This method requires the accurate and efficient numerical evaluation of iterated surface integrals over both source and testing domains. In this paper, we propose a scheme for evaluating these 4-D interaction integrals between pairs of arbitrarily positioned and oriented elements. The approach is based on applying the surface Divergence Theorem twice, once on the source and once on the test domain. When the integrations are reordered as two outer contour integrals plus two inner radial integrals, the initial radial integrations provide significant smoothing of the underlying singular integrands. The method is numerically validated for static and dynamic kernels arising in the electric field integral equation, i.e., for kernels with $1/R$ singularities, and linear basis functions. The proposed formula to evaluate 4-D reaction integrals can be extended to different kernels and to different elements, e.g., to curved or volumetric elements, and to basis functions of higher order.

Gang Yang - One of the best experts on this subject based on the ideXlab platform.

  • A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities
    International Journal for Numerical Methods in Engineering, 2016
    Co-Authors: Detao Wan, Sundararajan Natarajan, Stéphane Bordas, Gang Yang
    Abstract:

    In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian Divergence Theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub-triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion.

  • a novel integration scheme for solution of consistent mass matrix in free and forced vibration analysis
    Meccanica, 2016
    Co-Authors: Gang Yang, Detao Wan
    Abstract:

    The solution of mass matrix is one of the important parts for dynamic analysis of finite element method (FEM). In general FEM procedure, the numerical integration of consistent mass matrix needs to carry out the same operation as the stiffness matrix, which includes the coordinate mapping and computing of Jacobian matrix. There has been proposed smoothed finite element method for evaluating stiffness matrix to avoid the coordinate mapping and computing of Jacobian matrix in the numerical integration. In this work, a novel integration scheme is proposed to calculate the consistent mass matrix, in which a symbolic integration is implemented by combining indefinite integral with Gauss Divergence Theorem. Then, the novel integration scheme of consistent mass matrix is incorporated with the smoothing strain technique for free and forced vibration analysis. The accuracy and the convergence properties of the present method are investigated by several numerical examples. It can be concluded from the numerical results that the present method is robust and stability for dynamic analysis.

F Vipiana - One of the best experts on this subject based on the ideXlab platform.

  • 6 d mom reaction integrals evaluated via the Divergence Theorem
    International Conference on Electromagnetics in Advanced Applications, 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this contribution we propose an accurate and efficient numerical evaluation of 6-D reaction integrals that appear in the Method of Moment (MoM) discretization of Volume Integral Equations (VIEs).

  • Evaluation of 6-D MoM Integrals by Application of the Divergence Theorem with Singularity Subtraction Acceleration
    2021 15th European Conference on Antennas and Propagation (EuCAP), 2021
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    We propose to evaluate the double-volumetric integrals appearing in MoM formulations for volumetric integral equations by applying the Divergence Theorem to reduce both source and test integrals to surface integrals. Their integrands consist of the original kernel, basis, and test functions integrated twice radially in closed form. Implementing the surface integrals directly in the physical domain eliminates the restrictions to well-shaped elements. For faceted volumetric elements, the surface integrals reduce to the evaluation of interaction integrals between source and test face pairs. Triangular facets may be either integrated directly in barycentric coordinates or in a cylindrical coordinate system whose axis is the line of intersection of planes containing source and test face pairs. Further smoothing of the integrand is provided by first removing the static asymptotic form of the integrand from the integral, then restoring its contribution as a closed form integral whose removal accelerates convergence of the difference integral.

  • reducing the dimensionality of 6 d mom integrals applying twice the Divergence Theorem
    European Conference on Antennas and Propagation, 2020
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In this paper we propose a scheme for evaluating the 6-D interaction integrals appearing in volume integral equation solved with the Method of Moments and tetrahedral elements. We treat as a whole the double volume integral, applying the Divergence Theorem first on the source domain and then on the test domain. With the proper variable transformation and reordering, the 6-D integrals are expressed as two radial integrals plus four linear integrals over the source and observation domain planes.

  • acceleration of volume volume 6 d integrals for numerical evaluation by double application of the Divergence Theorem
    2019 International Applied Computational Electromagnetics Society Symposium (ACES), 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    In the present paper, we propose the application of the surface Divergence Theorem for the integration of double volumetric integrals for both source and test domain of the 6-D reaction integrals. The resulting 6-D volume integrals are expressed as two radial integrals plus two surface integrals over the source and observation domain boundaries. The radial integrations in the physical domain should be well-behaved and easily performed for arbitrary polyhedral domains. The method is numerically validated for static and dynamic kernels arising in the Electric Field Integral Equation (EFIE), i.e., for kernels with 1/R singularities, and linear basis functions.

  • evaluation of 4 d reaction integrals via double application of the Divergence Theorem
    IEEE Transactions on Antennas and Propagation, 2019
    Co-Authors: J Rivero, F Vipiana, D R Wilton, W A Johnson
    Abstract:

    The use of the method of moments to solve surface integral equations is one of the most popular numerical techniques in electromagnetic modeling and analysis. This method requires the accurate and efficient numerical evaluation of iterated surface integrals over both source and testing domains. In this paper, we propose a scheme for evaluating these 4-D interaction integrals between pairs of arbitrarily positioned and oriented elements. The approach is based on applying the surface Divergence Theorem twice, once on the source and once on the test domain. When the integrations are reordered as two outer contour integrals plus two inner radial integrals, the initial radial integrations provide significant smoothing of the underlying singular integrands. The method is numerically validated for static and dynamic kernels arising in the electric field integral equation, i.e., for kernels with $1/R$ singularities, and linear basis functions. The proposed formula to evaluate 4-D reaction integrals can be extended to different kernels and to different elements, e.g., to curved or volumetric elements, and to basis functions of higher order.