Numerical conformal mapping methods for simply and doubly connected regions

Journal Article · Thu Jan 01 00:00:00 EST 1998 · SIAM Journal on Scientific Computing

DOI:https://doi.org/10.1137/S1064827596303545· OSTI ID:599812

Delillo, T K ^[1]; Pfaltzgraff, J A ^[2]

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1. Wichita State Univ., KS (United States). Dept. of Mathematics and Statistics
2. Univ. of North Carolina, Chapel Hill, NC (United States). Dept. of Mathematics

Methods are presented and analyzed for approximating the conformal map from the interior (exterior) of the disk to the interior (exterior) of a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. The authors show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.

• Sponsoring Organization: USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
• DOE Contract Number: FG02-92ER25124
• OSTI ID: 599812
• Journal Information: SIAM Journal on Scientific Computing, Vol. 19, Issue 1; Other Information: PBD: Jan 1998
• Country of Publication: United States
• Language: English

Related Subjects

99 MATHEMATICS
COMPUTERS
INFORMATION SCIENCE
MANAGEMENT
LAW
MISCELLANEOUS
CONFORMAL MAPPING
NUMERICAL SOLUTION
BOUNDARY-VALUE PROBLEMS
MATHEMATICAL OPERATORS
CONVERGENCE