Vol. 2, No. 2, 2020
Download this article
Download this article For screen
For printing
Recent Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 3
Volume 6, Issue 2
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 2578-5885 (online)
ISSN 2578-5893 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the solution of Laplace's equation in the vicinity of triple junctions

Jeremy Hoskins and Manas Rachh
Vol. 2 (2020), No. 2, 447–476
DOI: 10.2140/paa.2020.2.447
Abstract

We characterize the behavior of solutions to systems of boundary integral equations associated with Laplace transmission problems in composite media consisting of regions with polygonal boundaries. In particular we consider triple junctions, i.e., points at which three distinct media meet. We show that, under suitable conditions, solutions to the boundary integral equations in the vicinity of a triple junction are well-approximated by linear combinations of functions of the form tβ, where t is the distance of the point from the junction and the powers β depend only on the material properties of the media and the angles at which their boundaries meet. Moreover, we use this analysis to design efficient discretizations of boundary integral equations for Laplace transmission problems in regions with triple junctions and demonstrate the accuracy and efficiency of this algorithm with a number of examples.

PDF Access Denied

We have not been able to recognize your IP address 216.73.216.116 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
boundary integral equations, multiple junction interfaces, corners, singular solutions, potential theory
Mathematical Subject Classification 2010
Primary: 31A10, 35Q60, 45L05, 65E05, 65R20
Milestones
Received: 1 August 2019
Revised: 12 February 2020
Accepted: 16 March 2020
Published: 22 May 2020
Authors
Jeremy Hoskins
Applied Mathematics Program
Yale University
New Haven, CT
United States
Manas Rachh
Center for Computational Mathematics
Flatiron Institute
New York, NY
United States