• Advantages of the boundary element method and meshless approaches are inherited in hybrid MDDM to deal with crack problems. Cracked Reissner's plate non homogenous media is investigated by first time. High accurate/convergent solutions using Chebyshev polynomials can be obtained . Growing applications non-homogenous engineering structures require application powerful computational tools. A no...

When undertaking a numerical solution of Helmholtz problems using the Boundary Element Method (BEM) it is common to employ low-order Lagrange polynomials, or more recently Non-Uniform Rational B-Splines (NURBS), as basis functions. A popular alternative for high frequency use an enriched basis, such plane wave used in Partition Unity (PUBEM). To authors’ knowledge there yet be thorough quantifi...

Abstract. Stochastic Collocation (SC) has been studied and used in different disciplines for Uncertainty Quantification (UQ). The method consists of computing a set of appropriate points, called collocation points, and then using Lagrange interpolation to construct the probability density function (pdf) of the quantity of interest (QoI). The collocation points are usually chosen as Gauss quadra...

This report is concerned with the computation cost of the determinant of a (bivariate) polynomial matrix required in the guaranteed accuracy L∞-norm computation. The obtained computation cost is in terms of word operations, unlike most results available in the literature where the computation cost is provided in terms of arithmetic operations. The proposed method employs multivariate Lagrange i...

A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given. Afterwards, several applications are presented. First a global construction of monotonic and/or convex generalized splines interpolating monotonic and/or co...

The aim of this paper is to generalize the Euler-Lagrange equation obtained in Almeida et al. (2011), where fractional variational problems for Lagrangians, depending on fractional operators and depending on indefinite integrals, were studied. The new problem that we address here is for cost functionals, where the interval of integration is not the whole domain of the admissible functions, but ...

In this paper, we propose and analyze an orthogonal non-polynomial nodal basis on triangles for discontinuous spectral element methods (DSEMs) for solving Maxwell’s equations. It is based on the standard tensor product of the Lagrange interpolation polynomials and a “collapsing” mapping between the standard square and the standard triangle. The basis produces diagonal mass matrices for the DSEM...

We use the Lagrange-Bürmann inversion theorem to characterize the generating function of the central coefficients of the elements of the Riordan group of matrices. We apply this result to calculate the generating function of the central elements of a number of explicit Riordan arrays, defined by rational expressions, and in two cases we use the generating functions thus found to calculate the H...

Mallows and Riordan “The Inversion Enumerator for Labeled Trees,” Bulletin of the American Mathematics Society, vol. 74 119681 pp. 92-94) first defined the inversion polynomial, JJ9) for trees with n vertices and found its generating function. In the present work, we define inversion polynomials for ordered, plane, and cyclic trees, and find their values at 9 = 0, t l . Our techniques involve t...

An efficient hybrid method is developed to approximate the solution of the high-order nonlinear Volterra-Fredholm integro-differential equations. The properties of hybrid functions consisting of block-pulse functions and Lagrange interpolating polynomials are first presented. These properties are then used to reduce the solution of the nonlinear Volterra-Fredholm integro-differential equations ...