Numerical Conformai Mapping
نویسندگان
چکیده
A numerical procedure to determine the discrete conformai 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 conformai 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.
منابع مشابه
A Numerical Comparison of Integral Equations of the First and Second Kind for Conformai Mapping
Two methods for computing numerical conformai mappings are compared. The first, due to Symm, uses a Fredholm integral equation of the first kind while the other, due to Lichtenstein, uses a Fredholm integral equation of the second kind. The two methods are tested on ellipses with different ratios of major to minor axes. The method based on the integral equation of the second kind is superior if...
متن کاملOn the Area Distortion by Quasiconformal Mappings
We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane. Astala [1] proved the following theorem conjectured by Gehring and Reich in [3]: Theorem A. Let f be a K-quasiconformal mapping of D = {z: \z\ < 1} onto itself with f(0) = 0. Then for any measurable E c D we have \f(E)\<C(K)\E\xlK, where \ • \ stands for the area. The first author [2] obtaine...
متن کاملA Transcendental View of the Space of Algebraic Riemann Surfaces
The subject of my lecture is not a large-scale and general theory but rather a special problem in conformai mapping. By way of justification for bringing it to the attention of a broader audience I may cite, first of all, its deep nature and honorable origin—the problem originated in Riemann's memoir [46] of 1857 on algebraic functions, and after the passage of a century some definitive insight...
متن کاملSine Function Quadrature Rules for the Fourier Integral
In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformai Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.
متن کاملNumerical Applications of Reflection to Partial Differential Equations
Recent papers have reported results on the numerical solution of nonlinear free boundary problems wherein a conformai transformation (which must be determined) maps the unknown flow region onto a known domain; the boundary conditions are handled by the method of steepest descent. The present paper discusses the use of the reflection property of solutions of elliptic equations to determine these...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010