The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering

  title={The Decoupled Potential Integral Equation for Time‐Harmonic Electromagnetic Scattering},
  author={Felipe Vico and Miguel Ferrando and Leslie Greengard and Zydrunas Gimbutas},
  journal={Communications on Pure and Applied Mathematics},
We present a new formulation for the problem of electromagnetic scattering from perfect electric conductors. While our representation for the electric and magnetic fields is based on the standard vector and scalar potentials A,φ in the Lorenz gauge, we establish boundary conditions on the potentials themselves rather than on the field quantities. This permits the development of a well‐conditioned second‐kind Fredholm integral equation that has no spurious resonances, avoids low‐frequency… 

A decoupled potential integral equation for the impedance boundary value problem

  • F. Vico
  • Mathematics
    2017 International Conference on Electromagnetics in Advanced Applications (ICEAA)
  • 2017
The electromagnetic impedance boundary value problem is very important in the electromagnetic literature [1, 2]. We adapt the decoupled potential integral equation DPIE [3] for the problem of

Robust multiscale field-only formulation of electromagnetic scattering

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the

Decoupled Potential Integral Equations for Electromagnetic Scattering From Dielectric Objects

Recent work on developing novel integral equation formulations has involved using potentials as opposed to fields as unknown variables. This is a consequence of additional flexibility offered by

Robust Field-Only Surface Integral Equations: Scattering from a Perfect Electric Conductor

A robust field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton–Chu formulation. For scattering by a perfect

Field-only surface integral equations: scattering from a perfect electric conductor.

A field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation, which allows high-order elements with fewer degrees of freedom to represent surface features to a higher precision than the traditional planar elements.

Formulation and Iso-Geometric Analysis of Scalar Integral Equations for Electromagnetic Scattering

Traditional integral equation-based models for field scattering start with defining an equivalent current on the surface of an object and then conditions on the tangential components of the fields.

Vector Potential Electromagnetics with Generalized Gauge for Inhomogeneous Media: Formulation (Invited Paper)

The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic

An Electric field based low frequency stable integral equation method for multiply connected perfect conductors

We present a new method to solve the Electric field scattered by a perfect electric conductor that is stable in low frequency and multiply connected geometries. The method is closely related to a

Decoupled Potential Integral Equation for Electromagnetic Scattering From Arbitrarily Shaped Dielectric Objects

Recently, integral equation formulations that use potentials as opposed to fields as unknown quantities have been developed for scattering from dielectric objects. It has been shown that these

Decoupled field integral equations for electromagnetic scattering from homogeneous penetrable obstacles

ABSTRACT We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in



Debye Sources and the Numerical Solution of the Time Harmonic Maxwell Equations II

In this paper, we develop a new integral representation for the solution of the time harmonic Maxwell equations in media with piecewise constant dielectric permittivity and magnetic permeability in

Current and charge Integral equation formulation

A new stable frequency domain surface integral equation formulation is proposed for the three dimensional electromagnetic scattering of composite metallic and dielectric objects. The developed

On a Well-Conditioned Electric Field Integral Operator for Multiply Connected Geometries

All known integral equation techniques for simulating scattering and radiation from arbitrarily shaped, perfect electrically conducting objects suffer from one or more of the following shortcomings:

Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering

A new version of the combined field integral equation (CFIE) for the solution of electromagnetic scattering problems in three dimensions is introduced, meaning that it is a second kind integral equation that does not suffer from spurious resonances and does not become ill conditioned for fine discretizations.

Overcoming Low-Frequency Breakdown of the Magnetic Field Integral Equation

In the electromagnetics literature, significant attention has been paid to the problem of low-frequency breakdown in the electric field integral equation. By contrast, the magnetic field integral

Boundary integral equation analysis on the sphere

The selection of certain parameters in “combined field” and “Calderon-preconditioned” formulations is shown to have a significant impact on condition number, extending earlier work by Kress and others.

Integral equation solution of Maxwell's equations from zero frequency to microwave frequencies

A permutation of the loop-tree or loop-star currents by a connection matrix is proposed, to arrive at a current basis that yields a MoM matrix that can be solved efficiently by iterative solvers.

On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies

The treatment of boundary value problems for Helmholtz equation and for the time harmonic Maxwell's equations by boundary integral equations leads to integral equations of the second kind which are

Magnetic field integral equation at very low frequencies

It is known that there is a low-frequency breakdown problem when the method of moments (MOM) with Rao-Wilton-Glisson (RWG) basis is used in the electric field integral equation (EFIE); it can be