We present a high-order spectral element method for solving layered media scattering problems featuring an operator that transparently enforces the far-field boundary condition. The incorporation of this Dirichlet-to-Neumann (DtN) map into the spectral element framework is a novel aspect of this work, and the resulting method can accommodate plane-wave radiation of arbitrary angle of incidence....

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a ...

This paper is concerned with the hp-version of the finite element method (hp-FEM) to treat a variational inequality that models frictional contact in linear elastostatics. Such an approximation of higher order leads to a nonconforming discretization scheme. We employ Gauss-Lobatto quadrature for the approximation of the nonsmooth frictiontype functional and take the resulting quadrature error i...

A numerical test case demonstrates that Lobatto and Gauss points are not natural superconvergent points for cubic and quartic finite elements under equilateral triangular mesh. 2000 Mathematics Subject Classification. Primary 65N30, Secondary 65N15, 41A10, 41A25, 41A27, 41A63.

In this paper Gauss-Radau and Gauss-Lobatto quadrature rules are presented to evaluate the rational integrals of the element matrix for a general quadrilateral. These integrals arise in finite element formulation for second order Partial Differential Equation via Galerkin weighted residual method in closed form. Convergence to the analytical solutions and efficiency are depicted by numerical ex...

This paper first presents a Gauss Legendre quadrature method for numerical integration of I 1⁄4 R R T f ðx; yÞdxdy, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)j0 6 x, y 6 1, x + y 6 1} in the Cartesian two dimensional (x,y) space. We then use a transformation x = x(n,g), y = y(n,g) to change the integral I to an equivalent integral R R S f ðxðn;...

Abstract In this article, different types of Gaussian quadrature methods have been presented to find the numerical integration a neutrosophic valued function. A new definition distance between two number has defined and it proved that set all form complete metric space. Also, continuity on closed-bounded interval in sense $$(\alpha ,\beta ,\gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/...

Barycentric interpolation is arguably the method of choice for numerical polynomial interpolation. The polynomial interpolant is expressed in terms of function values using the so-called barycentric weights, which depend on the interpolation points. Few explicit formulae for these barycentric weights are known. In [H. Wang and S. Xiang, Math. Comp., 81 (2012), 861–877], the authors have shown t...

Measurement of transient pressure distribution on maritime structures is important for the assessment hydrodynamic loads applied. The commonly used sensors are mostly bulky, need to be bolted structure, and/or only provide point-wise measurements. In this paper, an elastic matrix layer with a network embedded piezoelectric proposed address these issues. For experimental validation, 400 × 5 mm e...