Computational Analysis of Complicated Metamaterial Structures using MLFMA and Nested Preconditioners

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.