Search results for "Integral equations"
showing 10 items of 24 documents
Controlled time integration for the numerical simulation of meteor radar reflections
2016
We model meteoroids entering the Earth[U+05F3]s atmosphere as objects surrounded by non-magnetized plasma, and consider efficient numerical simulation of radar reflections from meteors in the time domain. Instead of the widely used finite difference time domain method (FDTD), we use more generalized finite differences by applying the discrete exterior calculus (DEC) and non-uniform leapfrog-style time discretization. The computational domain is presented by convex polyhedral elements. The convergence of the time integration is accelerated by the exact controllability method. The numerical experiments show that our code is efficiently parallelized. The DEC approach is compared to the volume …
Quadrature rules for qualocation
2003
Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988-2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions Gα form a Chebyshev–system on [0, 1/2] for arbitrary indices a and thus prove the existence of such quadrature rules for any J.
Fixed Point Theorems in Partially Ordered Metric Spaces and Existence Results for Integral Equations
2012
We derive some new coincidence and common fixed point theorems for self-mappings satisfying a generalized contractive condition in partially ordered metric spaces. As applications of the presented theorems, we obtain fixed point results for generalized contraction of integral type and we prove an existence theorem for solutions of a system of integral equations.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Fractional Derivatives in Interval Analysis
2017
In this paper, interval fractional derivatives are presented. We consider uncertainty in both the order and the argument of the fractional operator. The approach proposed takes advantage of the property of Fourier and Laplace transforms with respect to the translation operator, in order to first define integral transform of interval functions. Subsequently, the main interval fractional integrals and derivatives, such as the Riemann–Liouville, Caputo, and Riesz, are defined based on their properties with respect to integral transforms. Moreover, uncertain-but-bounded linear fractional dynamical systems, relevant in modeling fractional viscoelasticity, excited by zero-mean stationary Gaussian…
Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies
2017
An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…
Numerical modelling of electromagnetic sources by integral formulation
2012
Analysis of electromagnetic (EM) transients can be carried out by employing a eld approach in frequency domain, based on an appropriate integral equation. This approach is a powerful method for the analysis of EM antennas and scatterers. Recent work by the authors in modeling electromagnetic scattering in frequency domain are summarized. Thin-wire electric eld integral equation has been handled and possible application in obtaining sources localization information are discussed. Moments method (MoM) is used and time domain analysis is also carried out by discrete Fourier transform. Di erent approaches have been considered by using direct MoM formulation. Simulation results obtained both via…
Wavelet-like bases for thin-wire integral equations in electromagnetics
2005
AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…
A novel boundary element formulation for anisotropic fracture mechanics
2019
Abstract A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is …
Boundary Element Method for Composite Laminates
2017
The boundary element method (BEM) is a numerical technique to solve engineering/physical problems formulated in terms of boundary integral equations. Composite laminates are assemblages of stacked different materials layers, generally consisting of variously oriented fibrous composite materials