A transform method for Laplace's equation in multiply connected circular domains
File(s)
Published version
Author(s)
Crowdy, DG
Type
Journal Article
Abstract
A new general transform method for the solution of mixed boundary value problems for Laplace’s equation
in multiply connected circular domains is formulated. Circular domains are those with boundaries
that are a union of circular arcs and/or straight line segments. Constructive schemes based on the method
are showcased by application to some concrete problems in fluid mechanics. In particular, a boundary
value problem of topical interest in the study of superhydrophobic surfaces is solved and compared with
an existing numerical solution.
in multiply connected circular domains is formulated. Circular domains are those with boundaries
that are a union of circular arcs and/or straight line segments. Constructive schemes based on the method
are showcased by application to some concrete problems in fluid mechanics. In particular, a boundary
value problem of topical interest in the study of superhydrophobic surfaces is solved and compared with
an existing numerical solution.
Date Issued
2015-12-01
Date Acceptance
2015-06-21
Citation
IMA Journal of Applied Mathematics, 2015, 80 (6), pp.1902-1931
ISSN
0272-4960
Publisher
Oxford University Press (OUP)
Start Page
1902
End Page
1931
Journal / Book Title
IMA Journal of Applied Mathematics
Volume
80
Issue
6
Copyright Statement
© The authors 2015. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Grant Number
EP/K019430/1
Subjects
Science & Technology
Physical Sciences
Mathematics, Applied
Mathematics
transform method
multiply connected
Laplace's equation
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0199 Other Mathematical Sciences
Applied Mathematics
Publication Status
Published
Date Publish Online
2015-08-13