A Software Package for Computing Schwarz-Christoffel Conformal Transformation for Doubly Connected Polygonal Regions

this paper from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping "difficult" regions (to be specified in Section 2), and being user-friendly. Several examples are presented to demonstrate the capabilities of the package. Categories and Subject Descriptors: G.1.m [Numerical Analysis]: Miscellaneous; G.4 [Mathematics of Computing]: Mathematical Software-efficiency, reliability, and robustness General Terms: Algorithms Additional Key Words and Phrases: Numerical Conformal Mapping, Schwarz-Christoffel conformal transformation, doubly connected region, accessory parameters, system of nonlinear equations 2 This work was partially supported by NSF grant OSR-9255223 under the NSF EPSCOR Program when the author was working on his dissertation at Wichita State University. The paper as well as the major revision of the package were done at Fort Hays State University where the author is currently on its faculty. 1. INTRODUCTIO

Dataless Objects Considered Harmful

data type. A class specifies an abstract data type encapsulating both data and operations performed on that data; Operations construction. Operations are implemented using a language construct called (in Java) method. While the signature (or parameter list) of a method may vary significantly, methods are characterized in two ways: value-returning and void; Instance attributes. Without its instance attributes being specified, an object is meaningless; that is, the method setMessage must be called before any other method is invoked, though constructors are normally used to initialize values of instance data; Classes for different purposes. Whereas the class Message is used to specify a blueprint for making concrete messages (objects), the other class (MyFirstProgram) is used simply to satisfy a Java language requirement that the "main" method be wrapped in a public class; Main method. The main method, for which the syntax may change from one language to another, is where the program flow is defined (in this case, where messages are processed); and Reusability. Messages are reusable for making new messages, and methods are generally reusable. Moreover, this representation example is easily extended to addressing inheritance (for example, an email message or a memo can be derived by adding more relevant attributes to a message that includes only a message body) and polymorphism (for example, an email or a memo can have its own version of printMessage). The reason the author of [3] suggested his version of "Hello, World" was his concern that novices would unlearn PO programming, a popular justification for teaching objects-first in university programming courses. However, teaching dataless objects fundamentally defeats the notion of teaching objects-first. Aside from th..

Algorithm 785: A software package for computing Schwarz–Christoffel conformal transformation for doubly connected polygonal regions

A software package implementing Schwarz-Christoffel Conformal transformation (or mapping) of doubly connected polygonal regions is fully described in this article from mathematical, numerical, and practical perspectives. The package solves the so-called accessory parameter problem associated with the mapping function as well as evaluates forward and inverse maps. The robustness of the package is reflected by the flexibility in choosing the accuracy of the parameters to be computed, the speed of computation, the ability of mapping "difficult" regions (to be specified in Section 2), and being user friendly. Several examples are presented to demonstrate the capabilities of the package

Equilibrium configurations of point vortices in doubly connected domains

Point vortex flows of a steady, two dimensional, inviscid, and incompressible fluid are studied for doubly connected geometries. The Routh function is explicitly constructed, and equilibrium configurations of vortices are found by determining critical points numerically. The numerical computations make use of an analogue of the Schwarz-Christoffel transformation for doubly connected regions

Equilibrium Configurations of Point Vortices in Doubly Connected Domains

Point vortex flows of a steady, two dimensional, inviscid, and incompressible fluid are studied for doubly connected geometries. The Routh function is explicitly constructed, and equilibrium configurations of vortices are found by determining critical points numerically. The numerical computations make use of an analogue of the Schwarz-Christoffel transformation for doubly connected regions. 1 Introduction Consider a two-dimensional motion of an incompressible and inviscid fluid in a multiply connected two-dimensional region R. The boundary of R is assumed to consist of piecewise analytic curves \Gamma k (k = 0; 1; :::; m) with the external boundary, if there is one, denoted by \Gamma 0 . The motion is assumed to be irrotational except for a number of free point vortices with strength i at points P i (i = 1; 2; :::; n) . We assume further that all boundaries are fixed, the motion is steady at infinity, and no external forces act. Therefore the streamfunction for the motion does not ..