An iterative procedure for numerical conformal mapping is presented
which imposes no restriction on the boundary complexity. The formulation
involves two analytically equivalent boundary integral equations
established by applying the conjugation operator to the real and
the imaginary parts of an analytical function. The conventional approach
is to use only one and ignore the other equation. However, the discrete
version of the operator using the boundary element method (BEM) leads
to two non-equivalent sets of linear equations forming an over-determined
system. The generalised conjugation operator is introduced so that
both sets of equations can be utilised and their least-square solution
determined without any additional computational cost, a strategy
largely responsible for the stability and efficiency of the proposed
method. Numerical tests on various samples including problems with
cracked domains suggest global convergence, although this cannot
be proved theoretically. The computational efficiency appears significantly
higher than that reported earlier by other investigators.
%0 Journal Article
%1 Li1998
%A Li, Bao Cheng
%A Syngellakis, Stavros
%C Boston, MA, USA
%D 1998
%I American Mathematical Society
%J Mathematics of Computation
%K imported
%N 222
%P 619--639
%R http://dx.doi.org/10.1090/S0025-5718-98-00957-0
%T Numerical conformal mapping based on the generalised conjugation
operator
%U http://www.ams.org/mcom/1998-67-222/S0025-5718-98-00957-0/S0025-5718-98-00957-0.pdf
%V 67
%X An iterative procedure for numerical conformal mapping is presented
which imposes no restriction on the boundary complexity. The formulation
involves two analytically equivalent boundary integral equations
established by applying the conjugation operator to the real and
the imaginary parts of an analytical function. The conventional approach
is to use only one and ignore the other equation. However, the discrete
version of the operator using the boundary element method (BEM) leads
to two non-equivalent sets of linear equations forming an over-determined
system. The generalised conjugation operator is introduced so that
both sets of equations can be utilised and their least-square solution
determined without any additional computational cost, a strategy
largely responsible for the stability and efficiency of the proposed
method. Numerical tests on various samples including problems with
cracked domains suggest global convergence, although this cannot
be proved theoretically. The computational efficiency appears significantly
higher than that reported earlier by other investigators.
@article{Li1998,
abstract = {An iterative procedure for numerical conformal mapping is presented
which imposes no restriction on the boundary complexity. The formulation
involves two analytically equivalent boundary integral equations
established by applying the conjugation operator to the real and
the imaginary parts of an analytical function. The conventional approach
is to use only one and ignore the other equation. However, the discrete
version of the operator using the boundary element method (BEM) leads
to two non-equivalent sets of linear equations forming an over-determined
system. The generalised conjugation operator is introduced so that
both sets of equations can be utilised and their least-square solution
determined without any additional computational cost, a strategy
largely responsible for the stability and efficiency of the proposed
method. Numerical tests on various samples including problems with
cracked domains suggest global convergence, although this cannot
be proved theoretically. The computational efficiency appears significantly
higher than that reported earlier by other investigators.},
added-at = {2011-03-27T19:47:06.000+0200},
address = {Boston, MA, USA},
author = {Li, Bao Cheng and Syngellakis, Stavros},
biburl = {https://www.bibsonomy.org/bibtex/2f6c3cda2007a43b9f9608f7af9fca6a2/cocus},
doi = {http://dx.doi.org/10.1090/S0025-5718-98-00957-0},
file = {:./S0025-5718-98-00957-0.pdf:PDF},
interhash = {caf5ad072777dfc90a3bf2135b651f46},
intrahash = {f6c3cda2007a43b9f9608f7af9fca6a2},
issn = {0025-5718},
journal = {Mathematics of Computation},
keywords = {imported},
number = 222,
pages = {619--639},
publisher = {American Mathematical Society},
timestamp = {2011-03-27T19:47:10.000+0200},
title = {Numerical conformal mapping based on the generalised conjugation
operator},
url = {http://www.ams.org/mcom/1998-67-222/S0025-5718-98-00957-0/S0025-5718-98-00957-0.pdf},
volume = 67,
year = 1998
}