Integral equations requiring small numbers of Krylov-subspace iterations for two-dimensional smooth penetrable scattering problems Yassine Boubendir New Jersey Institute of Technology, boubendi@njit.edu Oscar Bruno Caltech, obruno@caltech.edu David Levadoux ONERA, david.levadoux@onera.fr Catalin Turc New Jersey Institute of Technology, catalin.c.turc@njit.edu Abstract This paper presents a class of boundary integral equations for the solution of prob- lems of electromagnetic and acoustic scattering by two dimensional homogeneous penetrable scatterers with smooth boundaries. The new integral equations, which, as is established in this paper, are uniquely solvable Fredholm equations of the sec- ond kind, result from representations of fields as combinations of single and double layer potentials acting on appropriately chosen regularizing operators. As demon- strated in this text by means of a variety of numerical examples (that resulted from a high-order Nystr¨ om computational implementation of the new equations), these “regularized combined equations” can give rise to important reductions in com- putational costs, for a given accuracy, over those resulting from previous iterative boundary integral equation solvers for transmission problems. Key words: Electromagnetic Scattering, Transmission Problems, Combined Field Integral Equations, Pseudo-differential Operators, Regularizing Operators 1991 MSC: 65R20, 35E99, 45B05, Preprint submitted to Elsevier © 2015. This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/