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Massimo Guiggiani - One of the best experts on this subject based on the ideXlab platform.

  • Galerkin BEM with Direct Evaluation of Hypersingular Integrals
    Electronic Journal of Boundary Elements, 2007
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is presented for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.

  • Direct Evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is developed for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is, not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.

  • Direct Evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is developed for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is, not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise. (C) 2003 Elsevier Science B.V. All rights reserved

  • Boundary element analysis of Kirchhoff plates with Direct Evaluation of hypersingular integrals
    International Journal for Numerical Methods in Engineering, 1999
    Co-Authors: Attilio Frangi, Massimo Guiggiani
    Abstract:

    The typical Boundary Element Method (BEM) for fourth-order problems, like bending of thin elastic plates, is based on two coupled boundary integral equations, one strongly singular and the other hypersingular. In this paper all singular integrals are evaluated Directly, extending a general method formerly proposed for second-order problems. Actually, the Direct method for the Evaluation of singular integrals is completely revised and presented in an alternative way. All aspects are dealt with in detail and full generality, including the Evaluation of free-term coe cients. Numerical tests and comparisons with other regularization techniques show that the Direct Evaluation of singular integrals is easy to implement and leads to very accurate results. Copyright ? 1999 John Wiley & Sons, Ltd.

  • Direct Evaluation of Hypersingular Integrals in 2D BEM
    Numerical Techniques for Boundary Element Methods, 1992
    Co-Authors: Massimo Guiggiani
    Abstract:

    A general Direct method for the Evaluation of hypersingular integrals in the BEM is presented with reference to two-dimensional problems. It is first shown that there are no special problems in the derivation of hypersingular boundary integral equations (HBIE’s), that is, in taking the singular point on the boundary. No unbounded quantities ultimately arise if the limiting process is properly performed. In the second part, the limit is expressed in terms of intrinsic coordinates. This is maybe the most critical step since the effects of the mapping must be accounted for. Then, the use of suitable expansions allows all singular integration to be performed analytically, even if curved higher-order boundary elements are employed. The original hypersingular integral is thus shown to be equivalent to some simple computable terms.

Marc Bonnet - One of the best experts on this subject based on the ideXlab platform.

  • Galerkin BEM with Direct Evaluation of Hypersingular Integrals
    Electronic Journal of Boundary Elements, 2007
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is presented for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.

  • Direct Evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is developed for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is, not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise.

  • Direct Evaluation of double singular integrals and new free terms in 2D (symmetric) Galerkin BEM
    Computer Methods in Applied Mechanics and Engineering, 2003
    Co-Authors: Marc Bonnet, Massimo Guiggiani
    Abstract:

    In this paper a new general algorithm is developed for the Direct Evaluation of all singular double integrals arising in the 2D Galerkin BEM, including those with hypersingular kernels. A distinguishing feature of the proposed method is that double singular integrals are treated as a whole, that is, not as inner integrals followed by outer ones. Therefore, when applied to the symmetric Galerkin BEM, the proposed technique is strictly symmetry preserving. Moreover, a careful analysis of the limiting process is performed which shows that some new free terms may arise. (C) 2003 Elsevier Science B.V. All rights reserved

Athanasios G Polimeridis - One of the best experts on this subject based on the ideXlab platform.

  • On the Direct Evaluation of Surface Integral Equation Impedance Matrix Elements Involving Point Singularities
    IEEE Antennas and Wireless Propagation Letters, 2011
    Co-Authors: Athanasios G Polimeridis, Juan R. Mosig
    Abstract:

    The Direct Evaluation method tailored to the 4-D singular integrals over vertex adjacent triangles, arising in the first-kind and second-kind Fredholm surface integral equation formulations, is presented. A combination of singularity cancellation, reordering of the integrations, and one analytical integration results in 3-D integrals of sufficiently smooth functions, allowing a straightforward computation by standard Gaussian rules. Numerical results demonstrate that the uncertainty about the accuracy of the impedance matrix elements associated to the interaction of vertex adjacent triangles is safely removed.

  • Fast and Accurate Computation of Hypersingular Integrals in Galerkin Surface Integral Equation Formulations via the Direct Evaluation Method
    IEEE Transactions on Antennas and Propagation, 2011
    Co-Authors: Athanasios G Polimeridis, J. M. Tamayo, Juan M. Rius, Juan R. Mosig
    Abstract:

    Hypersingular 4-D integrals, arising in the Galerkin discretization of surface integral equation formulations, are computed by means of the Direct Evaluation method. The proposed scheme extends the basic idea of the singularity cancellation methods, usually employed for the regularization of the singular integral kernel, by utilizing a series of coordinate transformations combined with a reordering of the integrations. The overall algebraic manipulation results in smooth 2-D integrals that can be easily evaluated via standard quadrature rules. Finally, the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency.

  • analysis of numerical integration in the Evaluation of hyper singular integrals in galerkin surface integral equation formulations via the Direct Evaluation method
    European Conference on Antennas and Propagation, 2010
    Co-Authors: J. M. Tamayo, Athanasios G Polimeridis, Juan M. Rius, A Heldring, J R Mosig
    Abstract:

    In this paper, some aspects of the Direct Evaluation method for the computation of hyper-singular 4-D integrals, arising in the Galerkin discretization of surface integral formulations, are analyzed. In its original version, utilizing a series of coordinate transformations combined with a re-ordering of the integrations, the integrand not only was regularized but also it was casted in a convenient form in order to perform two dimensions of the integrals analytically. Here, we are going to test and compare the behavior when only one or none of the dimensions is held analytically. Furthermore, the importance of the re-ordering will be outlined, even when no analytical integration is performed.

  • on the Direct Evaluation of weakly singular integrals in galerkin mixed potential integral equation formulations
    IEEE Transactions on Antennas and Propagation, 2008
    Co-Authors: Athanasios G Polimeridis, T V Yioultsis
    Abstract:

    Weakly singular integrals over coincident triangles, arising in the Galerkin discretization of mixed potential integral equation formulations, are calculated using a Direct Evaluation method. The proposed method utilizes a series of coordinate transformations, together with a re-ordering of the integrations, in order to reduce the dimensionality of the original four-dimensional (4D) weakly singular integrals into 1D numerical integrations of smooth functions. The final formulas can be easily evaluated with a standard Gaussian quadrature rule, resulting in a scheme with great accuracy and efficiency properties. Numerical results for the comparison of the proposed method with both singularity subtraction and singularity cancellation methods, often used for the Evaluation of multidimensional singular integrals, are presented, indicating the superior overall performance of the Direct Evaluation scheme.

Juan R. Mosig - One of the best experts on this subject based on the ideXlab platform.

  • On the Direct Evaluation of Surface Integral Equation Impedance Matrix Elements Involving Point Singularities
    IEEE Antennas and Wireless Propagation Letters, 2011
    Co-Authors: Athanasios G Polimeridis, Juan R. Mosig
    Abstract:

    The Direct Evaluation method tailored to the 4-D singular integrals over vertex adjacent triangles, arising in the first-kind and second-kind Fredholm surface integral equation formulations, is presented. A combination of singularity cancellation, reordering of the integrations, and one analytical integration results in 3-D integrals of sufficiently smooth functions, allowing a straightforward computation by standard Gaussian rules. Numerical results demonstrate that the uncertainty about the accuracy of the impedance matrix elements associated to the interaction of vertex adjacent triangles is safely removed.

  • Fast and Accurate Computation of Hypersingular Integrals in Galerkin Surface Integral Equation Formulations via the Direct Evaluation Method
    IEEE Transactions on Antennas and Propagation, 2011
    Co-Authors: Athanasios G Polimeridis, J. M. Tamayo, Juan M. Rius, Juan R. Mosig
    Abstract:

    Hypersingular 4-D integrals, arising in the Galerkin discretization of surface integral equation formulations, are computed by means of the Direct Evaluation method. The proposed scheme extends the basic idea of the singularity cancellation methods, usually employed for the regularization of the singular integral kernel, by utilizing a series of coordinate transformations combined with a reordering of the integrations. The overall algebraic manipulation results in smooth 2-D integrals that can be easily evaluated via standard quadrature rules. Finally, the reduction of the dimensionality of the original integrals together with the smooth behavior of the associated integrands lead up to unmatched accuracy and efficiency.

Guillermo J. Creus - One of the best experts on this subject based on the ideXlab platform.

  • Direct Evaluation of singular integrals in boundary element analysis of thick plates
    Engineering Analysis with Boundary Elements, 2002
    Co-Authors: Rogério José Marczak, Guillermo J. Creus
    Abstract:

    Abstract This work presents the derivation of the asymptotic expansions for two dimensional elasticity and plate bending problems fundamental solutions, applied to the Direct Evaluation of BEM singular integrals. Interesting conclusions arise from the resulting analytical expressions, regarding the actual order of singularity of the kernel functions. The expansions were tested for a number of plate bending benchmarks, showing good agreement to analytical solutions for thin and thick plates. The convergence behavior for constant, linear and quadratic elements is analyzed and compared with other integration techniques.