Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Open Access Guideline
Open Access Guideline
Postgraduate Thesis Guideline
Postgraduate Thesis Guideline
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Implementation of the equivalence principle algorithm for potential integral equations
Download
index.pdf
Date
2018
Author
Farshkaran, Ali
Metadata
Show full item record
Item Usage Stats
228
views
172
downloads
Cite This
In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalence principle algorithm (EPA) is described for solving arbitrary shaped perfect electric conductor (PEC) and penetrable objects. The main advantage of EPA is its efficiency thanks to the enhanced conditioning hence accelerated iterative solutions of the matrix equations derived from discretizations. For further enhancing the efficiency, the multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplications (MVMs) in EPA. Following standard implementations, a novel implementation of EPA using potential integral equations (PIEs) is further presented. EPA is generalized to be compatible with PIEs used to formulate inner problems inside equivalence surfaces. Based on the stability of PIEs at low frequencies, the resulting EPA-PIE implementation is suitable for low-frequency problems involving dense discretizations with respect to wavelength. Along with the formulation and demonstration of the EPA-PIE scheme, high accuracy and stability of the implementation are presented on canonical problems.
Subject Keywords
Integral equations.
,
Huygens' principle.
URI
http://etd.lib.metu.edu.tr/upload/12622305/index.pdf
https://hdl.handle.net/11511/27392
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
Evaluation of Hypersingular Integrals on Non-planar Surfaces
Selcuk, Gokhun; Koç, Seyit Sencer (2014-05-16)
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....
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation employing the Green’s function. The Rayleigh- Ritz method is applied to the integral-equation formulation of the one-dimensional Schrödinger equation in order to approximate the eigenvalues of the corresponding singular problem within the desired accuracy. The outcomes are compared with those r...
Modified Combined Tangential Formulation for Stable and Accurate Analysis of Plasmonic Structures
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-03-30)
We present a modified combined tangential formulation (MCTF) for stable solutions of plasmonic problems involving metallic objects that are modeled as penetrable structures. For a wide range of negative real permittivity values, corresponding to the varying characteristics of the metals at infrared and visible frequencies, MCTF provides both accurate and efficient solutions in comparison to the conventional formulations. We explain the stability of MCTF in terms of the discretized operators for the limit ca...
Hybrid Surface Integral Equations for Optimal Analysis of Perfectly Conducting Bodies
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2015-07-24)
We consider hybrid formulations involving simultaneous applications of the electric-field integral equation (EFIE), the magnetic-field integral equation (MFIE), and the combined-field integral equation (CFIE) for the electromagnetic analysis of three-dimensional conductors with arbitrary geometries. By selecting EFIE, MFIE, and CFIE regions on a given object, and optimizing these regions in accordance with the simulation requirements, one can construct an optimal hybrid-field integral equation (HFIE) that p...
Generalized Hybrid Surface Integral Equations for Finite Periodic Perfectly Conducting Objects
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-01-01)
Hybrid formulations that are based on simultaneous applications of diversely weighted electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) on periodic but finite structures involving perfectly conducting surfaces are presented. Formulations are particularly designed for closed conductors by considering the unit cells of periodic structures as sample problems for optimizing EFIE and MFIE weights in selected regions. Three-region hybrid formulations, which are designed by geneti...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
A. Farshkaran, “Implementation of the equivalence principle algorithm for potential integral equations,” M.S. - Master of Science, Middle East Technical University, 2018.
