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Sauter Finite elements on degenerate meshes: inverse-type inequalities and applications. IMA, J. Schwab Randelementmethoden Book, pp. Remangen: World Scientific, pp. Feistauer, V. Dolejsi, P. Knobloch, K. Najzar , Springer, Berlin, pp. Part 1: Scalar Elliptic Problems Comp. Wittum Bridging the gap between geometric and algebraic multi-grid methods Computing and Visualization in Science, Vol 6 1 , pp. Analysis with Boundary Elem. Lage Transformation of hypersingular integrals and black-box cubature Mathematics of Computation, Vol 70, pp.

Bonnet, A.

Small Modifications of Quadrature Domains

Saendig, W. Eds, pp. Bungartz, R. Hoppe, C.

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Zenger, Springer-Verlag, Heidelberg pp. Sauter Variable order panel clustering Computing, Vol 64 3 , pp. Sauter A panel clustering method for 3-d elastostatics using spherical harmonics In: "Integral methods in science and engineering", Eds.

Small Modifications of Quadrature Domains

Bertram, C. Constanda and A. Sauter Boundary integral equation for second order elliptic boundary value problems Preprint Nr. Wrobel, S. Chandler-Wilde, Eds. Warnke Extension operators and approximation on domains containing small geometric details East-West J. Sauter Fast integration techniques in 3D boundary elements. Numerical results indicated that the accuracy of the calculated results is improved significantly by employing the modified generalized differential quadrature method.

The concept of differential quadrature method introduced by Bellman and Casti and Bellman et al.

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The differential quadrature method has been shown to be a powerful contender in solving initial and boundary value problems and thus has become an alternative to the existing methods. Chen and Zhong pointed out that the differential quadrature method and the differential cubature method, due to their global domain property, are more efficient for nonlinear problems than the traditional numerical techniques such as finite element method and finite difference method. One of the fields among which can find extensive applications of the differential quadrature method is structural mechanics.

Civan solved multivariable mathematical model s using differential quadrature method and differential cubature method. Malik and Bert implemented the differential quadrature method multiple boundary conditions to free vibration of plates. In order to derive the weighting coefficients in a more explicit way, a generalized differential quadrature method was proposed by Quan and Chang a, b.

They presented that the generalized differential quadrature method is rather convenient in comparison with the differential quadrature method. Hua and Lam pointed out that generalized differential quadrature method is no restriction on the distribution and the number of discrete grid points used in the approximation process and the weighting coefficients are determined by using a simple recurrence relationship instead of by solving a set of linear algebraic equations. Dynamic characteristics of annular plates are of considerable importance in many designs.

Azimi a solved free vibration of circular plates with elastic edge supports using the receptance method. Azimi b solved free vibration of circular plates with elastic or rigid interior support. Wang et al. In this work, the generalized differential quadrature method is employed to formulate the discrete eigenvalue problems of annular plates.

In this study a different approach is proposed for applications of the boundary conditions using the modified generalized differential quadrature method. The integrity and computational efficiency of the modified generalized differential quadrature method in this problem will be demonstrated through a series of case studies.

For a function f r , generalized differential quadrature method approximation for the m order derivative at the ith sampling point is given by. The advantages of the generalized differential quadrature method over the differential quadrature method are that the general form of the test function is taken to be Lagrangian interpolation polynomial in order to determine the weighting coefficients instead of solving a set of linear algebraic equations.

The test function is.

Motivation

Other types of polynomials could be used as well. However, by using the Lagrangian interpolation polynomial, the numerical ill conditions in calculating the weighting matrix would be overcome. Introducing Eq. Once the sampling points are selected, the weighting matrix can easily be obtained from Eq. For the second order and higher order derivatives, the weighting coefficients are obtained by using the following simple recurrence relation.

It is emphasized that the number of the test functions must be greater than the highest order of derivative in the governing equations. The selection of locations of the sampling points plays a significant role in the accuracy of the solution of differential equations. For a domain separate into by N points, one could obtain equally spaced sampling points.

Inner points are. Boundary points are. Using equally spaced points can be considered to be a convenient and an easy selection method. For a domain separate into by N points, one could obtain a more accurate solution by choosing a set of unequally spaced sampling points. Bert and Malik pointed out simple and good choice can be the Chebyshev-Gauss-Lobatto points. Following nonuniform grid spacing gives better and more reliable results.

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