Implementation of the equivalence principle algorithm for potential integral equations

Farshkaran, Ali
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.


Color engineering of π-conjugated donor-acceptor systems : the role of donor and acceptor units on the neutral state color
Ünal, Gönül; Karasu, Atalay; Department of Physics (2011)
In this thesis, we investigate the integrability properties of some evolutionary type nonlinear equations in (1+1)-dimensions both with commutative and non-commutative variables. We construct the recursion operators, based on the Lax representation, for such equations. Finally, we question the notion of integrability for a certain one-component non-commutative equation. [We stress that calculations in this thesis are not original.]
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...
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 ...
Least-squares finite element solution of Euler equations with adaptive mesh refinement
Akargün, Hayri Yiğit; Sert, Cüneyt; Department of Mechanical Engineering (2012)
Least-squares finite element method (LSFEM) is employed to simulate 2-D and axisymmetric flows governed by the compressible Euler equations. Least-squares formulation brings many advantages over classical Galerkin finite element methods. For non-self-adjoint systems, LSFEM result in symmetric positive-definite matrices which can be solved efficiently by iterative methods. Additionally, with a unified formulation it can work in all flight regimes from subsonic to supersonic. Another advantage is that, the me...
Citation Formats
A. Farshkaran, “Implementation of the equivalence principle algorithm for potential integral equations,” M.S. - Master of Science, Middle East Technical University, 2018.