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Mathematics of Computation

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Numerical conformal mapping

Authors: Sukumar Chakravarthy and Dale Anderson
Journal: Math. Comp. 33 (1979), 953-969
MSC: Primary 30C30; Secondary 65E05
MathSciNet review: 528049
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Abstract: A numerical procedure to determine the discrete conformal mapping of an arbitrary simply connected region onto the open unit disk is described. The method is fast and directly provides an estimate of the global error due to the discretization of the mapping. The intimate relationship between the Riemann Mapping Theorem and the numerical method of construction of the conformal mapping is brought out in the presentation. The procedure is an interesting example of a method of construction that is directly based on a theorem guaranteeing existence and uniqueness.

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  • [1] I. H. ABBOTT & A. E. VON DOENHOFF, Theory of Wing Sections, Dover, New York, 1958.
  • [2] W. D. BARFIELD, "Numerical method for generating orthogonal curvilinear meshes," J. Computational Phys., v. 5, 1970, pp. 23-33.
  • [3] B. L. Buzbee, A capacitance matrix technique, Sparse matrix computations (Proc. Sympos., Argonne Nat. Lab., Lemont, Ill., 1975) Academic Press, New York, 1976, pp. 365–373. MR 0501805
  • [4] John B. Conway, Functions of one complex variable, 2nd ed., Graduate Texts in Mathematics, vol. 11, Springer-Verlag, New York-Berlin, 1978. MR 503901
  • [5] Anthony V. Fiacco and Garth P. McCormick, Nonlinear programming: Sequential unconstrained minimization techniques, John Wiley and Sons, Inc., New York-London-Sydney, 1968. MR 0243831
  • [6] R. Fletcher and C. M. Reeves, Function minimization by conjugate gradients, Comput. J. 7 (1964), 149–154. MR 187375,
  • [7] H. LOMAX & E. D. MARTIN, "Fast direct numerical solution of the nonhomogeneous Cauchy-Riemann equations," J. Computational Phys., v. 15, 1974, pp. 55-80.
  • [8] G. MORETTI, "Conformal mappings for computations of steady, three-dimensional, supersonic flows," in Numerical/Laboratory Computer Methods in Fluid Mechanics (Papers presented at the winter meeting of the ASME, New York, 1976), ASME, New York, 1976.
  • [9] M. J. D. Powell, A survey of numerical methods for unconstrained optimization, SIAM Rev. 12 (1970), 79–97. MR 258253,
  • [10] Roland A. Sweet, A generalized cyclic reduction algorithm, SIAM J. Numer. Anal. 11 (1974), 506–520. MR 520169,

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Keywords: Conformal mapping, numerical conformal mapping
Article copyright: © Copyright 1979 American Mathematical Society