The convergence of iterative solutions to the Electric Field Integral Equation

Convergence of iterative methods applied to Burgers-Huxley equation

Convergence of the Natural hp-BEM for the Electric Field Integral Equation on Polyhedral Surfaces

We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on divΓ-conforming Raviart-Thomas boundary elements (BEM) of locally variable polynomial degree on shape-regular surface meshes. We establish asymptotic quasi-optimality of Galerkin solutions on sufficiently fi...

Solving the Electric Field Integral Equation using a Sparse Approximate Inverse preconditioned iterative method

In this Master's Thesis we discuss the use of a modi ed Sparse Approximate Inverse method for preconditioning of the dense matrices arising in the Boundary Element Method when applied to the Electric Field Integral Equation. In particular we consider the case of a perfect electric conductor. Some general properties of the modi ed Sparse Approximate Inverse for complex symmetric problems are sho...

Discrete Fredholm properties and convergence estimates for the electric field integral equation

The Galerkin discretization of the Electric Field Integral Equation is reinvestigated. We prove quasi-optimal convergence estimates at nonresonant frequencies, using orthogonal splittings of the Galerkin space. At resonant frequencies we show that the spurious electric currents radiate only weakly in the exterior domain. This is achieved through the study of some finitely degenerated problems i...

The reduced basis method for the electric field integral equation

We introduce the Reduced Basis Method (RBM) as an efficient tool for parametrized scattering problems in computational electromagnetics for problems where field solutions are computed using a standard Boundary Element Method (BEM) for the parametrized Electric Field Integral Equation (EFIE). This combination enables an algorithmic cooperation which results in a two step procedure. The first ste...