TY - JOUR
T1 - The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains
AU - Araeo, j
AU - Bradshaw-Hajek, B
AU - Miklavcic, S
AU - Ward, Dale
PY - 2010
Y1 - 2010
N2 - Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.
AB - Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the method's strength and scope, we apply it to Laplace's equation on an annular-like domain.
UR - http://www.scopus.com/inward/record.url?scp=77951235696&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/43/18/185202
DO - 10.1088/1751-8113/43/18/185202
M3 - Article
SN - 0305-4470
VL - 43
SP - 1
EP - 18
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 18
M1 - 185202
ER -