TY - JOUR

T1 - An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes

AU - Vico, Felipe

AU - Greengard, Leslie

AU - Ferrando-Bataller, Miguel

AU - Antonino-Daviu, Eva

N1 - Funding Information:
Manuscript received November 26, 2016; revised August 20, 2018; accepted August 23, 2018. Date of publication January 8, 2019; date of current version April 5, 2019. This work was supported in part by the Spanish Ministry of Science and Innovation under Project TEC2016-78028-C3-3-P and in part by the Office of the Assistant Secretary of Defense for Research and Engineering and AFOSR through the NSSEFF Program under Award FA9550-10-1-0180. (Corresponding author: Felipe Vico.) F. Vico, M. Ferrando-Bataller, and E. Antonino-Daviu are with the Institute of Telecommunications and Applications Multimedia, Polytechnic University of Valencia, 46022 Valencia, Spain (e-mail: felipe.vico@gmail.com; mferrand@dcom.upv.es; evanda@upvnet.upv.es).
Publisher Copyright:
© 1963-2012 IEEE.

PY - 2019/4

Y1 - 2019/4

N2 - We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancelation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumann-type boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, nonresonant, and well conditioned at all frequencies. A principal advantage of our approach, by contrast with the hypersingular electric field integral equation, the combined field integral equation, or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method. Furthermore, the formalism is compatible with nonconformal mesh discretization and works well with singular (sharp) boundaries.

AB - We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancelation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumann-type boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, nonresonant, and well conditioned at all frequencies. A principal advantage of our approach, by contrast with the hypersingular electric field integral equation, the combined field integral equation, or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method. Furthermore, the formalism is compatible with nonconformal mesh discretization and works well with singular (sharp) boundaries.

KW - Calderon preconditioning (CP)

KW - Maxwell equations

KW - charge-current formulations

KW - electromagnetic (EM) scattering

KW - high-frequency preconditioning

UR - http://www.scopus.com/inward/record.url?scp=85059802269&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85059802269&partnerID=8YFLogxK

U2 - 10.1109/TAP.2019.2891399

DO - 10.1109/TAP.2019.2891399

M3 - Article

AN - SCOPUS:85059802269

VL - 67

SP - 2513

EP - 2521

JO - IEEE Transactions on Antennas and Propagation

JF - IEEE Transactions on Antennas and Propagation

SN - 0018-926X

IS - 4

M1 - 8605366

ER -