Improving Iterative Solutions of the Electric-Field Integral Equation Via Transformations Into Normal Equations

Generalized Combined Field Integral Equations for the Iterative Solution of the Helmholtz Equation in Three Dimensions

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of acoustic scattering problems. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the wel...

Generalized Combined Field Integral Equations for the Iterative Solution of the Three-dimensional Helmholtz Equation

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be...

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...

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...

Improving the Accuracy of the Solutions of Riccati Equations