Evaluation of Hypersingular Integrals on Non-planar Surfaces

Date

2014-05-16

Author

Selcuk, Gokhun
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

166
views

0
downloads

Solving electric field integral equation (EFIE) with Nystrom method requires accurate evaluation of hypersingular surface integrals since this method does not use divergence conforming basis and testing functions. The success of the method also depends on accurate representation of non-planar characteristics of the scattering object. In this study Hadamard finite part interpretation is used to evaluate hypersingular integrals over non-planar surfaces, which are represented by their Taylor series expansions. Numerical tests are conducted to show the effectiveness of the formulas. Also a scattering problem is solved which confirms the accuracy.

Subject Keywords

EFIE, Nystrom method, Hypersingular integral, Hadamard finite part

URI

https://hdl.handle.net/11511/54887

Conference Name

International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO)

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Evaluation of Hypersingular Integrals on Curvilinear Surface Elements Selcuk, Gokhun; Koç, Seyit Sencer (2016-04-15) In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystriim (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined ...
An Efficient Semianalytical Method for Hypersingularity Treatment Over Curved Patches Selcuk, G.; Koç, Seyit Sencer (2017-05-01) In this communication, we propose an efficient method to evaluate hypersingular integrals defined on curved surfaces. First an exact expression for hypersingular kernel is derived by projecting the integral on curvilinear element on a flat surface. Next singularity subtraction employed, where the singular core is hypersingular and the remaining part is weakly singular. The singular core is evaluated analytically using finite part interpretation and the remaining weakly singular part is evaluated numerically...
Solution of Volume Integral Equations with Novel Treatment to Strongly Singular Integrals Selcuk, Gokhun; Kurt, Sinan; Koç, Seyit Sencer (2015-05-17) Locally corrected Nystrom (LCN) method is applied for the solution of volume integral equations (VIEs). Unlike the conventional method of moments (MoM) procedure, LCN method does not use divergence conforming basis and testing functions to reduce the order of singularity of the integrand. Therefore LCN method needs to handle kernels with higher order singularities. For VIEs, worst singularity is due to the double derivative operator acting on free space Green's function and resulting integrals are referred ...
Implementation and assessment of modern shock-capturing schemes for hypersonic viscous flows Şahin, Çağatay; Baran, Özgür Uğraş; Atik, Hediye; Department of Mechanical Engineering (2022-8-22) Spatially second order accurate Finite Volume Method (FVM) is the most preferred method in Computational Fluid Mechanics (CFD) with its acceptable results in short computation times. FVM's accuracy heavily relies on the particular numerical scheme with which the fluxes are evaluated. Despite the maturity of traditional flux schemes today, simulations of a viscous hypersonic ﬂow are still challenging. Since these cases involve strong shock waves and viscous layers with non-linear gradients, appropriate shock...
Application of nyström method for the solution of time domain electric field integral equation Selçuk, Gökhun; Koç, Seyit Sencer; Department of Electrical and Electronics Engineering (2014) Solution of surface scattering problems with electric field integral equation (EFIE) requires careful treatment of singularities introduced by the 3D dyadic Green’s function when source and observation points are close to each other or coincide. One may either utilize the divergence conforming basis and testing functions to reduce the order of singularity or directly deal with singularities via analytical singularity extraction methods. The latter method is a not a commonly used one although it enables use ...

Citation Formats

G. Selcuk and S. S. Koç, “Evaluation of Hypersingular Integrals on Non-planar Surfaces,” presented at the International Conference on Numerical Electromagnetic Modeling and Optimization for RF, Microwave, and Terahertz Applications (NEMO), Pavia, Italy, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54887.