On the Errors Arising in Surface Integral Equations Due to the Discretization of the Identity Operator

On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems Ergül, Özgür Salih (null; 2006-11-10) We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...
Efficient preconditioning strategies for the multilevel fast multipole algorithm Gurel, Levent; Malas, Tahir; Ergül, Özgür Salih (2007-03-30) For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of MLFMA with the help of the flexible solvers. Among fixed preconditioners, we show that an incomplete LU precondition...
Modified Superformula Contours Optimized via Genetic Algorithms for Exponentially Converging 2D Solutions of MFIE Guler, Sadri; Onol, Can; Ergül, Özgür Salih; Sever, Emrah; Dikmen, Fatih; Tuchkin, Yury A. (2017-05-25) An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of magnetic field integral equation (MFIE) in 2D either for TM or TE polarized excitations. A version of superformula modified for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the MFIE kernel and convergence of the solution ...
On the errors arising in surface integral equations due to the discretization of the identity operatort Ergül, Özgür Salih (2009-06-05) Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficien...
On multiplication in finite fields Cenk, Murat; Özbudak, Ferruh (2010-04-01) We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...

Citation Formats

Ö. S. Ergül, “On the Errors Arising in Surface Integral Equations Due to the Discretization of the Identity Operator,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52958.