Combined Field Integral Equation-Based Theory of Characteristic Mode

Integral Equation Analysis with Characteristic Basis Functions

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

Combinations of simulation and integral equation theory

Much work has been done to accelerate the prediction of structure and thermodynamics, particularly of the chemical potential of condensed phases by means of molecular simulation, requiring large computational power or simpli®ed simulation procedures. This work demonstrates that the combination of simulation with approximate calculations based on integral equation theory provides the necessary i...

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...