CircularMap: A numerical implementation of the circular map in MATLAB
Copyright Mohamed Nasser 2017
Please cite this MATLAB functions as:
When citing this software please mention the URL of the master repository
(https://github.com/mmsnasser/CircularMap), and the paper
M.M.S. Nasser,Fast Computation of the Circular Map, Computational Methods
and Function Theory, 15 (2015) 187-223.
PLEASE note that this toolbox contains the files:
zfmm2dpart.m
fmm2d_r2012a.mexw32
fmm2d_r2012a.mexw64
pthreadGC2-w32.dll
pthreadGC2-w64.dll
From the Toolbox:
L. G REENGARD AND Z. G IMBUTAS , FMMLIB2D: A MATLAB toolbox for
fast multipole method in two dimensions, Version 1.2, 2012.
http://www.cims.nyu.edu/cmcl/fmm2dlib/fmm2dlib.html
PLEASE also cite the FMMLIB2D toolbox.
The function
[zet,zetp,cntd,rad] = circmap(et,etp,alpha,n)
Compute the circular map from a bounded multiply connected domain G of
connectivity m+1 bounded by \Gamma_0,\Gamma_1,...,\Gamma_m where \Gamma_0
is the exterior boundary onto a bounded multiply connected circular domain
\Omega bounded by the circles C_0,C_1,...,C_m where C_0 is the exterior circle
and C_0 is the unit circle. The function also Compute the circular map for
unbounded multiply connected circular domain of connectivity m bounded by
\Gamma_1,...,\Gamma_m onto an unbounded multiply connected domain \Omega
bounded by the circles C_1,...,C_m.
In particular, the function "circmap.m" compute
- cntd: a vector contains the centers of the circles C_0,C_1,...,C_m for
bounded G; and the centers of the circles C_1,...,C_m for unbounded G.
- rad: a vector contains the radius of the circles C_0,C_1,...,C_m for
bounded G; and the radius of the circles C_1,...,C_m for unbounded G.
-
zet: the parameterization of the boundary of \Omega.
-
zetp: the derivative of the parameterization of the boundary of \Omega where
-
et: the parameterization of the boundary of G.
-
etp: the derivative of the parameterization of the boundary of G
-
alpha: for bounded G, alpha is a point in G that will be mapped onto 0 in \Omega; for unbounded G, alpha=inf and it will be mapped onto inf.
-
n: the number of discretization points of each boundary component
-
koebetol: the tolerance of Koebe iterative method
-
gmrestol: the tolerance of GMRES iterative method
-
koebemaxit: the maximum number of iterations allowed for Koebe iterative method
-
gmresmaxit:the maximum number of iterations allowed for GMRES iterative method
-
iprec: for the accurecy of the FMM (see zfmm2dpart.m).