Conformal mapping of circular arc polygons
An algorithm is described which computes the conformal mapping from the unit disk onto an arbitrary polygon having circular arcs as sides. This generalizes the Schwarz-Christoffel program. The algorithm must also determine certain parameters by solving a nonlinear least squares problem. Instead of using Gauss-Jacobi quadrature to evaluate the Schwarz-Christoffel integral, however, an ordinary differential equation solver is applied to a non-singular formulation of the Schwarzian differential equation. The construction of a conformal mapping reduces simple elliptic partial differential equations on an irregular region to similar problems on a disk, for which existing programs can compute solutions very efficiently. Typical examples arise in the modeling of conductivity past an array of conducting cylinders and electrical fields inside a waveguide.
- Research Organization:
- Dept. of Computer Science, Univ. of Bergen, N-5000 Bergen
- OSTI ID:
- 6536775
- Journal Information:
- SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 8:1; ISSN SIJCD
- Country of Publication:
- United States
- Language:
- English
Similar Records
Jacobi splittings and the method of overlapping domains for solving elliptic P. D. E. 's
Conformal mapping and convergence of Krylov iterations
Related Subjects
990230* -- Mathematics & Mathematical Models-- (1987-1989)
ALGORITHMS
CIRCULAR CONFIGURATION
COMPUTER CODES
CONFIGURATION
CONFORMAL MAPPING
CYLINDERS
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
EQUATIONS
FUNCTIONS
GAUSS FUNCTION
JACOBIAN FUNCTION
LEAST SQUARE FIT
MAPPING
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
QUADRATURES
TOPOLOGICAL MAPPING
TRANSFORMATIONS
WAVEGUIDES