✦ LIBER ✦

Numerical treatment of the Cauchy integral equation by discrete Fourier transform

✍ Scribed by Valentina Kolybasova; Pavel Krutitskii; Konstantin Prozorov; Gennadi Vainikko

Publisher: Wiley (John Wiley & Sons)
Year: 2009
Tongue: English
Weight: 133 KB
Volume: 27
Category: Article
ISSN: 2040-7939
DOI: 10.1002/cnm.1336

No coin nor oath required. For personal study only.

✦ Synopsis

The uniquely solvable system of the Cauchy integral equation of the first kind and index 1 and an additional integral condition are treated. Such a system arises, for example, when solving the skew derivative problem for the Laplace equation outside an open arc in a plane. This problem models the electric current from a thin electrode in a semiconductor film placed in a magnetic field. A fast and accurate numerical method based on the discrete Fourier transform is proposed. Some computational tests are given. It is shown that the convergence is close to exponential.

📜 SIMILAR VOLUMES

On bicubic transformation for the numeri

On bicubic transformation for the numerical evaluation of Cauchy principal value integrals

✍ Chen, T. Charles 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB 👁 1 views

Recently a bicubic transformation was introduced to numerically compute the Cauchy principal value (CPV) integrals. Numerical results show that this new method converges faster than the conventional Gauss-Legendre quadrature rule when the integrand contains different types of singularity. Assume is

A superstable time-discrete scheme for t

A superstable time-discrete scheme for the numerical integration of viscous constitutive equations

✍ P. Royis 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 226 KB 👁 2 views

The general framework of the paper deals with the finite element modelling of mechanical problems involving viscous materials such as bitumen or bituminous concrete. Its aim is to present a second-orderaccurate discrete scheme which remains unconditionally superstable when used for the time discreti

A fast solution of the time-domain integ

A fast solution of the time-domain integral equation using fast Fourier transformation

✍ Jin-Lin Hu; Chi Hou Chan; Yuan Xu 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB 👁 2 views

In this paper, a fast algorithm that can be used to sol¨e the time-domain integral equation of transient wa¨e fields is presented. The technique discretizes the time-domain electric-field integral equation ( ) ( ) TDEFIE by means of the marching-on-in-time MOT method. The ( ) fast Fourier transforma

Investigation of numerical time-integrat

Investigation of numerical time-integrations of Maxwell's equations using the staggered grid spatial discretization

✍ I. Faragó; R. Horváth; W. H. A. Schilders 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 204 KB

The Yee-method is a simple and elegant way of solving the time-dependent Maxwell's equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound for the possible time-steps. This is why, during the last decade, the ma

Well-conditioned matrices for numerical

Well-conditioned matrices for numerical treatment of Fredholm integral equations of the second kind

✍ Giuseppe Mastroianni; Gradimir V. Milovanović 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 182 KB

Improved numerical method for the Tracti

Improved numerical method for the Traction Boundary Integral Equation by application of Stokes' theorem

✍ A. Young 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 164 KB 👁 2 views

This paper concerns the direct numerical evaluation of singular integrals arising in Boundary Integral Equations for displacement (BIE) and displacement gradients (BIDE), and the formulation of a Traction Boundary Integral Equation (TBIE) for solving general elastostatic crack problems. Subject to c