ROF FOR THE COMBINED FIELD INTEGRAL EQUATION

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...

Regularized Combined Field Integral Equations

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...

Coercive combined field integral equations

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...