Approximating the conformal maps of elongated quadrilaterals by domain decomposition

Constructive Approximation

Volumn 17, Issue 4, 2001, Pages 589-617

  Falcao M I ^a   Papamichael, N ^b   Stylianopoulos, N S ^b  

^a UNIVERSITY OF MINHO   (Portugal)

^b UNIVERSITY OF CYPRUS   (Cyprus)

Author keywords

Domain decomposition; Numerical conformal mapping; Quadrilaterals

Indexed keywords

EID: 0035537152     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003650010037     Document Type: Article

References (21)

1. L. V. AHLFORS (1973): Conformal Invariants: Topics in Geometric Function Theory. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill.
2. T. A. DRISCOLL (1996): Algorithm 657: A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans. Math. Soft., 22:168-186.
3. T. A. DRISCOLL, S. A. VAVASIS (1998): Numerical conformal mapping using cross-ratios and Delaunay triangulation. SIAM J. Sci. Comput., 19:1783-1803.
4. M. I. FALCÃO, N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1999): Curvilinear crosscuts of subdivision for a domain decomposition method in numerical conform mapping. J. Comput. Appl. Math., 106:177-196.
5. D. GAIER, W. K. HAYMAN (1990): Moduli of long quadrilaterals and thick ring domains. Rend. Math. Appl. (7), 10:809-834.
6. D. GAIER, W. K. HAYMAN (1991): On the computation of modules of long quadrilaterals. Constr. Approx., 7:453-467.
7. D. GAIER, N. PAPAMICHAEL (1987): On the comparison of two numerical methods for conformal mapping. IMA J. Numer. Anal., 7:261-282.
8. W. K. HAYMAN (1948): Remarks on Ahlfors' distortion theorem. Quart. J. Math. (Oxford), 19:33-53.
9. P. HENRICI (1986): Applied and Computational Complex Analysis, Vol. III. New York: Wiley.
10. D. M. HOUGH (1990): User's Guide to CONFPACK. IPS Research Report 90-11, ETH-Zentrum. CH-8092 Zurich, Switzerland.
11. L. H. HOWELL, L. N. TREFETHEN ( 1990): A modified Schwarz-Chrisroffel transformation for elongated regions. SIAM J. Sci. Statist. Comput., 11:928-949.
12. R. LAUGESEN (1994): Conformal mapping of long quadrilaterals and thick doubly connected domains. Constr. Approx., 10:523-554.
13. N. PAPAMICHAEL (1989): Numerical conformal mapping onto a rectangle with applications to the solution of Laplacian problems. J. Comput. Appl. Math., 28:63-83.
14. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1990): On the numerical performance of a domain decomposition method for conformal mapping. In: Computational Methods and Function Theory 1989, St. Ruscheweyh (E. B. Saff, L. C. Salinas, R. S. Varga, eds.). Lecture Notes in Mathematics, Vol. 1435. pp. 155-169. Berlin: Springer-Verlag.
15. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1991): A domain decomposition method for conformal mapping onto a rectangle. Constr. Approx., 7:349-379.
16. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1992): A domain decomposition method for approximating the conformal modules of long quadrilaterals. Numer. Math., 62:213-234.
17. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1994): On the theory and application of a domain decomposition method for computing conformal modules. J. Comput. Appl. Math., 50:33-50.
18. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1995): Domain decomposition for conformal maps. In: Computational Methods and Function Theory 1994 (R. M. Ali, St. Ruscheweyh, E. B. Saff. eds.), Ser. Approx. Decompos., Vol. 5, pp. 267-291. River Edge, NJ: World Scientific.
19. N. PAPAMICHAEL, N. S. STYLIANOPOULOS (1999): The asymptotic behavior of conformal modules of quadrilaterals with applications to the estimation of resistance values. Constr. Approx., 15:109-134.
20. L. N. TREFETHEN (1980): Numerical computation of the Schwarz-Christoffel transformation. SIAM J. Sci. Statist. Comput., 1:82-102.
21. L. N. TREFETHEN (1989): SCPACK User's Guide. Numerical Analysis Report 89-2. Department of Mathematics, MIT. Cambridge, MA.