A Novel Numerical Method for Evaluation of Hypersingular Integrals in Electromagnetics

Date

2015-11-28

Author

Selcuk, Gokhun
Demir, Oguz
Koç, Seyit Sencer

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

210
views

0
downloads

In this study we develop a numerical method for evaluation of hypersingular surface integrals, which arise in the solution of electric field integral equation (EFIE) via Nystrom method. Due to the divergent contribution of an infinitesimal area around the singular point, hypersingular integrals are told to be numerically intractable and analytical methods are employed for evaluation of these integrals. In this study we interpret hypersingular integrals as the second order derivative of weakly singular integrals, which can be efficiently evaluated using quadrature rules. By evaluating the derivative of weakly singular integrals numerically, we have shown that hypersingular integrals can accurately be evaluated using the proposed method. We have solved a scattering problem via Nystrom method to confirm the validity of the method.

URI

https://hdl.handle.net/11511/52757

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

An integral equation approach to the computation of nonlinear fields in electrical machines Kükrer, Osman; Ertan, H. Bülnet (Institute of Electrical and Electronics Engineers (IEEE), 1988-7) A numerical method based on an integral equation formulation, for the computation of nonlinear magnetostatic field, in two dimensions in cylindrical polar coordinates is given. The correctness of the method is illustrated by solving two linear two-dimensional magnetic field problems which have readily available analytical solutions. The dependence of the accuracy of the solution on the number and distribution of the meshes is studied on these examples. The method is then applied to the computation of the no...
A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind Kaya, Ruşen; Taşeli, Hasan (2022-01-01) A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
An algorithm for estimating Box–Cox transformation parameter in ANOVA Dag, Osman; İlk Dağ, Özlem (Informa UK Limited, 2016-8-5) In this study, we construct a feasible region, in which we maximize the likelihood function, by using Shapiro-Wilk and Bartlett's test statistics to obtain Box-Cox power transformation parameter for solving the issues of non-normality and/or heterogeneity of variances in analysis of variance (ANOVA). Simulation studies illustrate that the proposed approach is more successful in attaining normality and variance stabilization, and is at least as good as the usual maximum likelihood estimation (MLE) in estimat...
A discontinuous subgrid eddy viscosity method for the time-dependent Navier-Stokes equations Kaya Merdan, Songül (Society for Industrial & Applied Mathematics (SIAM), 2005-01-01) In this paper we provide an error analysis of a subgrid scale eddy viscosity method using discontinuous polynomial approximations for the numerical solution of the incompressible Navier-Stokes equations. Optimal continuous in time error estimates of the velocity are derived. The analysis is completed with some error estimates for two fully discrete schemes, which are first and second order in time, respectively.
An algebraic method for the analytical solutions of the Klein-Gordon equation for any angular momentum for some diatomic potentials Akçay, Hüseyin; Sever, Ramazan (IOP Publishing, 2014-01-01) Analytical solutions of the Klein-Gordon equation are obtained by reducing the radial part of the wave equation to a standard form of a second-order differential equation. Differential equations of this standard form are solvable in terms of hypergeometric functions and we give an algebraic formulation for the bound state wave functions and for the energy eigenvalues. This formulation is applied for the solutions of the Klein-Gordon equation with some diatomic potentials.

Citation Formats

G. Selcuk, O. Demir, and S. S. Koç, “A Novel Numerical Method for Evaluation of Hypersingular Integrals in Electromagnetics,” 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52757.