In this paper we describe a method for computing the Discrete Fourier Transform (DFT) of a sequence of n elements over a finite field GF(pm) with a number of bit operations 0(nm log(nm) ■ P(q)) where P(q) is the number of bit operations required to multiply two q-bit integers and q = 2 log2« + 4 log2m + 4 log2p. This method is uniformly applicable to all instances and its order of complexity is...

The cracking elements method (CEM) is a novel numerical approach for simulating fracture of quasi-brittle materials. This method is built in the framework of conventional finite element method (FEM) based on standard Galerkin approximation, which models the cracks with disconnected cracking segments. The orientation of propagating cracks is determined by local criteria and no explicit or implic...

x2 + y2. Note that |z| is the distance of z from 0. Also note that |z|2 = zz. The complex exponential function e is defined to be equal to cos(θ)+ i sin(θ). Note that e is a point on the unit circle, x + y = 1. Any complex number z can be written in the form re where r = |z| and θ is an appropriately chosen angle; this is sometimes called the polar form of the complex number. Considered as a fu...

The Cahn–Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C-continuous basis functions. In the current work, a quantitative comparison between C Hermi...

In this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming (SOCP) for the minimization problem. Three different C-discontinuous finite elements are considered : the quadratic 6 node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble ...

In this paper, we introduce the Petrov-Galerkin method for solution of stochastic Volterra integral equations. Here, we use continues Lagrange-type k-0 elements, since these elements have simple structure and via them, the solution of stochastic Volterra integral equation is reduced to algebraic equations. Also the error analysis of this method is done. In Comparison with other methods, this me...

We propose a new space efficient operator to multiply elements lying in a binary field F2k . Our approach is based on a novel system of representation called Double Polynomial System which set elements as a bivariate polynomials over F2. Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a spac...

• Asymptotics of the Lebesgue constant for Lagrange interpolation based on Lissajous-Chebyshev node points. partial sums Fourier series generated by anisotropically dilated rhombus. Formula Dirichlet kernel with frequencies in In this paper asymptotic formulas are given constants three special approximation processes related to ? 1 -partial series. particular, we consider polynomials points, rh...