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A new closed-form formula for calculating a weakly singular static potential integral with linear current source distribution on a triangle

Grytsko Anna, Słobodzian Piotr

Bulletin of the Polish Academy of Sciences. Technical Sciences

2023

Vol. 71, nr 1

art. no. e143645

The article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a triangular domain into a double integral, and then directly determining formulas for the inner and outer integrals. The solution obtained is marked by high computational efficiency, high accuracy, and very simple implementation. The derived formula, in contrast to the currently available formulas, consists of quantities that have a clear and simple geometric interpretation, related to the geometry of the computational domain.

Approximation solution for singular integral equations with logarithmic kernel using adapted linear spline

Nadir M.

Journal of Theoretical and Applied Computer Science

2016

Vol. 10, nr 1

19--25

In this work, we apply a direct method for an approximative solution of a weakly singular integral equations (W.S.I.E) with logarithmic kernel on an oriented smooth contour using a modified linear spline approximation, we also show that this approximation gives an efficient approach to the analytical solution of (W.S.I.E)

A modified linear approximation for weakly singular integrals

Nadir M.

Journal of Theoretical and Applied Computer Science

2015

Vol. 9, nr 4

19--25

In this work, we present a new approximation for a weakly singular integral, in particular Abel's integral. This approximation is based on the modification of the linear spline function, this one leads to eliminate the weak singularity. Noting that, it is clear that in the future we use this approximation for solving numerically all weakly singular integrals equations on an oriented smooth curve or on an interval.

Adapted quadratic approximation for logarithmic kernel integrals

Nadir M.

Fasciculi Mathematici

2012

Nr 49

75--85

In this work, we explain a new numerical schemes of collocation methods based on the adapted quadratic approximation of singular integral with logarithmic kernel. This approximation leads to obtain the numerical solution of singular integral equations with logarithmic kernel on an oriented smooth contour.