Solution of Volume Integral Equations with Novel Treatment to Strongly Singular Integrals

Selcuk, Gokhun
Kurt, Sinan
Koç, Seyit Sencer
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 to strongly singular integrals. Using finite part interpretation, we converted strongly singular integrals to regular integrals, for the solution of which conventional numerical methods can be applied. We have solved a three-dimensional scattering problem from a dielectric cube and showed the validity of the method.


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....
Solution of the nonlinear diffusion equation using the dual reciprocity boundary element method and the relaxation type time integration scheme
Meral, G (2005-03-18)
We present the combined application of the dual reciprocity boundary element method (DRBEM) and the finite difference method (FDM) with a relaxation parameter to the nonlinear diffusion equation: partial derivative u/partial derivative t = V del(2)u + p(u) at where p(u) is the nonlinear term. The DRBEM is employed to discretize the spatial partial derivatives by using the fundamental solution of the Laplace operator, keeping the time derivative and the nonlinearity as the nonhomogeneous terms in the equatio...
Solution of Navier-Stokes Equations Using FEM with Stabilizing Subgrid
Tezer, Münevver; Aydın Bayram, Selma (2009-07-03)
The Galerkin finite element method (FEM) is used for solving the incompressible Navier Stokes equations in 2D. Regular triangular elements are used to discretize the domain and the finite-dimensional spaces employed consist of piece wise continuous linear interpolants enriched with the residual-free bubble (RFB) functions. To find the bubble part of the solution, a two-level FEM with a stabilizing subgrid of a single node is described in our previous paper [Int. J. Numer. Methods Fluids 58, 551-572 (2007)]....
Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
Ergül, Özgür Salih (2009-06-05)
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary c...
Mitigating internal resonances of the magnetic-field integral equation via double-layer modeling
Güler, Sadri; İbili, Hande; Ergül, Özgür Salih (Institution of Engineering and Technology; 2018-04-13)
We present a new method to mitigate internal resonances of the magnetic-field integral equation (MFIE) for closed conductors, without combining this equation with the electric-field integral equation (EFIE) that is commonly practiced in the literature. For a given object and its surface, a smaller closed surface is placed inside to create a double layer. This way, the magnetic field intensity is enforced to zero on the inner surface, making the overall solution unique at all frequencies. By eliminating the ...
Citation Formats
G. Selcuk, S. Kurt, and S. S. Koç, “Solution of Volume Integral Equations with Novel Treatment to Strongly Singular Integrals,” 2015, Accessed: 00, 2020. [Online]. Available: