Talk:Electric-field integral equation

This is one of the best anonymous contributions I've ever seen. ✈ James C. 05:03, 2005 Jun 8 (UTC)

EFIE is a very powerful tool in computational electromagnetics. It also finds applications in acoustics. The EFIE also suffers from ill-conditioning - a topic of current research - Indranil Chowdhury(Univ. Washington).

This article definitely needs to be corrected

Someone should really correct this article - its factual content and the way it's written. First of all, there is virtually no introduction - what's the article about? I couldn't really figure out - the equations in the first paragraph are certainly not general Maxwell's equations of an electrodynamical field. Probably they are equations for a harmonic E-M wave, but it should be explicitly stated! Otherwise the reader may find it confusing to see things like "rot E = H" (!) etc. The notation is also unclear. The rest of article should be rewritten, because it's technical and and the same time vague.

--MichalKotowski (talk) 17:08, 10 March 2009 (UTC)

This article is not about the Electric Field Integral Equation !!

This article gives an integral representation of the electric field in terms of a distribution of electric current in free space. What one usually calls the electric field integral equation (EFIE), though, is an equation satisfied by the electric current distribution as the source of a scattered (or secondary) field when some material object with electric contrast is introduced in a given electromagnetic field. Among the many equations one can derive for such current distributions, the EFIE is the most immediately obtained, using the integral representation given in this article.

There are many misunderstandings in the interpretation section. This article is not written by someone who knows scattering theory very well and the author of the article does not seem to be particularly familiar with integral equations. It will need a complete rewrite to make it an article on the EFIE indeed. I hope to find some time in the future, in the mean time,

Readers be warned!

Bas Michielsen (talk) 15:43, 4 March 2008 (UTC)

I do not seeing anything glaringly wrong with the information presented in this article. The EFIE is an integral equation that relates the electric field excited by current sources that is directly applied to scattering problems with PEC scatters by virtue of the fact that the scattered and incident electric fields cancel other out on the surface of the scatterer. In which case you would simply substituted E^{i} for E and flip the sign on the integral in the given dyadic integral equation. The common approach to solving this problem is to use the Method of Moments or some other boundary element method. You can take a look at section 12.3 of Balanis' that is given in the references and Chew's book also contains the dyadic form. The given dyadic form is equivalent to the EFIE given in Balanis.

Born2bwire (talk) 02:23, 15 April 2008 (UTC)

OK then, here are some more detailed critical notes.

• The EFIE is not used to compute the electric field from a given current distribution, as the actual article states in its first line, but to compute a current distribution from a given electric field.
• The derivation section presents only a derivation of an integral representation. The domain of the electric field, in this representation, is not the domain of the current distribution. Therefore, the final result of the derivation is not an integral equation.
• The interpretation section again suggests that the EFIE is important in antenna theory because it allows one to compute radiated fields from given current distributions. However, the importance of the EFIE for antenna problems is that it allows one to find these current distributions from given antenna port excitations.
• The interpretation section also states that the MFIE and the CFIE contain resonances. But it does not say what that means. The CFIE, in fact, does not suffer from the internal resonance problem, but its discretised version can have bad condition numbers because its spectrum can touch zero.
• The interpretation section states that it is unfortunate that the EFIE relates the scattered field to J, which we do not know, and that this problem can be solved by imposing boundary conditions on the scattered field and on the incident field. However, boundary conditions are imposed on the total field and we are fortunate to have an EFIE relating the unknown J to the scattered field for which we can derive a boundary value by subtracting the known incident field from the total field.

To account for the above critics, I am thinking of a text like:

The Electric Field Integral Equation relates an electric current distribution to a given electric field. This integral equation arises in the analysis and solution of certain boundary value problems for the Maxwell partial differential equations. The EFIE is derived by requiring boundary values on an integral representation of the electric field in terms of current distributions. The integral representation is constructed with the use of a Green function such as to define vector valued functions satisfying the wave equation everywhere outside the support of the current distribution. It should be clear then that if one succeeds in finding a current distribution such that the boundary values are as given, the integral representation provides the solution of the boundary value problem.

The most frequently found example of such a boundary value problem defines the scattered field component in a time-harmonic electromagnetic scattering problem in an unbounded (exterior) domain with electrically impenetrable obstacles. In such cases, the EFIE is a boundary integral equation. The current distribution one tries to find then, is a distribution with support on the boundary of the obstacle and the given electric field is the negative of the boundary trace of the incident electric field. A time-harmonic boundary EFIE is not mathematically equivalent to the underlying boundary value problem because it can be shown that its integral operator is not invertible at frequencies for which the domain of the obstacle has so-called "interior resonances." The exterior boundary value problem for the scattered field has a unique solution for any frequency though. This "interior resonance" problem also appears with the Magnetic Field Integral Equation (MFIE). Linear combinations of the EFIE and the MFIE lead to the Combined Field Integral Equation (CFIE) which can be constructed to be invertible for all frequencies.

This text needs improvement, so please let me know what you think of this proposal. Bas Michielsen (talk) 23:25, 8 May 2008 (UTC)

Fredholm integral equation ?

I removed a remark saying that the EFIE is a Fredholm integral equation of the first kind "because" the current appears only under the integral. This is a, rather common, misunderstanding. Integral operators in the classical Fredholm theory are compact operators. The distinction between first kind and second kind Fredholm integral equations makes sense only if this restriction on the operators is respected. If the only criterion would be that the unknown "appears under the integral," a simple transformation of the Green function (adding a shifted Dirac distribution) would allow one to transform a first kind equation into a second kind equation and vice versa. In general, the singularity of the Green function determines whether the operator built on it is compact or not. Bas Michielsen (talk) 10:30, 3 March 2008 (UTC)

Heavy revision possible?

I'm a PhD student who works in this area (computational electromagnetics), and I spent the whole summer working through the electric field integral equation. The derivation done here is very different from that in much of the literature. I would like to do a serious overhaul of this derivation, and to provide a lot of context to it with example problems, if the community would appreciate it. Any thoughts?

Thanks. Brimacki (talk) 02:34, 23 September 2014 (UTC)

I would say, go ahead and make this article in something correct and readable. Thanks in advance. Bas Michielsen (talk) 07:22, 23 September 2014 (UTC)

Status

I came across this page and immediately wanted to edit it. After reading the talk comments it appears that someone has picked up the task but the most recent date is 9/2014. Based on the comments related to this article it seems like an EFIE specific page should at least reference a more general treatment that includes the MFIE and CFIE to address the resonance issue for closed surfaces. EFIE is sufficient for an open surface so this page stands alone but it definitely should be improved. Drdrbergman (talk) 15:03, 18 March 2016 (UTC)