New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here


by: Adaline Pollich


Marketplace > University of Kentucky > Electrical Engineering > EE 525 > NUMERICAL METHODS AND ELECTROMAGNETICS
Adaline Pollich
GPA 3.81

Stephen Gedney

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Stephen Gedney
Class Notes
25 ?




Popular in Course

Popular in Electrical Engineering

This 3 page Class Notes was uploaded by Adaline Pollich on Friday October 23, 2015. The Class Notes belongs to EE 525 at University of Kentucky taught by Stephen Gedney in Fall. Since its upload, it has received 8 views. For similar materials see /class/228316/ee-525-university-of-kentucky in Electrical Engineering at University of Kentucky.




Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/23/15
Evaluating the PVI of the MFIE The MFIE governing the induced electric current density on S is expressed as ingtltIjlmcFjFidngtltVgtltfGltF7F jF ds 1 S a where in is the outward unit normal to S at F r lies on 3 which is the closed surface just outside of S and r F dng 2 where 8 is a very small positive real number G is the free space Green s function de ned as 6W 139 Sing GR F JGI F 3 where R V 39 and the integral on the righthandside of 1 requires a principal value integral PVI Next apply the identity V X 3 Wow if F X va i 4 and note that a a R 8 R 1 763 e R I varr39 R la RU 73G 22 igR K R 3K 22 5 where RJF FF 7 F39 GR and G are de ned in 3 and kR sinltkR kR 39 kR 76R COS 7 KW smlt gt3wslt gt7 m g 6 km M then 1 is rewritten as 3 an X F H Z an gtlt fjF39XRKRR jKI 11ml ds39ds 7 7T 3 where we have assumed that in X RImc Fr in X TIME The dif culty lies when R gt 0 At this point 51quot XHS is discontinuous on S hence we can say that 51 X13 is dual valued In the limit that R gt0 K1012 713 and is a regular function On the other hand KRR is hypersingular in that in the limit as R gt 0 KRR a 00 as 1 R3 It is the presence and characteristic of this hypersingularity that leads to the dual value of 51quot X HS NeXtde ne F7FF ingiFFiF dng dng 8 Thus in the limit that 6 a 0 RI R Thus 7 can be rewritten as an X F i F k3 A V I E117 xii10 xRSKRR 31603 ds 9 lim an gtlt fi xeanlme jKIR ds39 5H0 47F S where the second term on the righthandside is referred to as the a principal value of the integral and the last term is the residual Since K1 is regular and bounded the contribution to the residual from this term is 0 in the limit that 6 a 0 On the other hand KR has a l R3 singularity Furthermore the triple cross product in X is X in is nonzero in the limit R a 0 Hence KR will have a nonzero contribution to the residual in the region near the hypersingularity Away from the singularity KR is smooth and consequently in the limit that 8 gt 0 will be zero Thus to evaluate the residual term we need only to evaluate this integral in the very near vicinity of R a 0 Here we will approximate S to be locally planar and will approximate the integral as that over a at disk of radius Ap centered by the origin at the eld point 7 Small argument approximations for the trigonometric functions are then applied shim M 0kR3 10 coskR 1 0kR2 The residual is then written as k3 AP 2quot A MR 1 Res 6113 ploq loean gtltJr39gtlt an kmg W pd gtdp 11 Next let R 422 62 and assume that jF39 z HF leading to 3 A k e l l Pv1 lim ed XJF39 gtltd pdp 6H0 2 n lt lt n jail kid2 62 k3ltp2 62 ilim gjFgti zi 1 AJZ 2 i quotAp2 2i 12 H02 l k kngAp2 2 J k3 a 1 1 1 a 1 7 7 J 39 0k 3 7511M Finally from 12 and 9 the MFIE is expressed as k3 A a R I I 13 Ean ng r XR K RK 1 ds where F is onSand R l 7 F39l Mor generally we can express the MFIE as A a a 1 a A e a aanmcr JrangtltJL VgtltGRJr39ds39 14 S where the integral representing the principal value is now de ned nonhypersingular and inte grabl e


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Kyle Maynard Purdue

"When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the I made $280 on my first study guide!"

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.