Browsing by Subject "Electric-field integral equation"

Now showing 1 - 3 of 3

Open Access
Computational analysis of complicated metamaterial structures using MLFMA and nested preconditioners
(IEEE, 2007-11) Ergül, Özgür; Malas, Tahir; Yavuz, Ç; Ünal, Alper; Gürel, Levent
We consider accurate solution of scattering problems involving complicated metamaterial (MM) structures consisting of thin wires and split-ring resonators. The scattering problems are formulated by the electric-field integral equation (EFIE) discretized with the Rao-Wilton- Glisson basis functions defined on planar triangles. The resulting dense matrix equations are solved iteratively, where the matrix-vector multiplications that are required by the iterative solvers are accelerated with the multilevel fast multipole algorithm (MLFMA). Since EFIE usually produces matrix equations that are ill-conditioned and difficult to solve iteratively, we employ nested preconditioners to achieve rapid convergence of the iterative solutions. To further accelerate the simulations, we parallelize our algorithm and perform the solutions on a cluster of personal computers. This way, we are able to solve problems of MMs involving thousands of unit cells.
Open Access
Singularity of the magnetic-field integral equation and its extraction
(Institute of Electrical and Electronics Engineers, 2005) Gürel, Levent; Ergül, Özgür
In the solution of the magnetic-field integral equation (MFIE) by the method of moments (MOM) on planar triangula-tions, singularities arise both in the inner integrals on the basis functions and also in the outer integrals on the testing functions. A singularity-extraction method is introduced for the efficient and accurate computation of the outer integrals, similar to the way inner-integral singularities are handled. In addition, various formulations of the MFIE and the electric-field integral equation are compared, along with their associated restrictions.
Open Access
The solution of large EFIE problems via preconditioned multilevel fast multipole algorithm
(Institution of Engineering and Technology, 2007) Malas, Tahir; Gürel, Levent
We propose an effective preconditioning scheme for the iterative solution of the systems formulated by the electric- field integral equation (EFIE). EFIE is notorious for producing difficult-to-solve systems. Especially, if the target is complex and the utilized frequency is high, it becomes a challenge to solve these dense systems with even robust solvers such as full GMRES. For this purpose, we use an inner-outer solver scheme and use an approximate multilevel fast multipole algorithm for the inner solver to provide a very efficient approximation to the dense linear system matrix. We explore approximation level and inner-solver accuracy to optimize the efficiency of the inner-outer solution scheme. We report the solution of large EFIE systems of several targets to show the effectiveness of the proposed approach.