This book presents a new numerical method of conformal mapping (the RT-algorithm) based on the R and T procedures. Solutions are given for arbitrary simply connected and doubly connected domains with piecewise - smooth contours. The continuum mechanics, including hydrodynamics, electrodynamics and elasticity theory.
The bool encompasses a wide range of numerical methods and computer techniques, including computer graphics. Problems analyzed are at the forefront of applied problems in modern technology.
Solutions to boundary-value problems on the unit circle and circular annulus are obtaines by systematic use of Taylor an Laurent series, the Ritz method, finite elements, and the conjugate-vortex method. Analytical solutions and experimental data are to verfy results of the numerical computations obtained by the RT-algorithm.
Preface.
Introduction.
Chapter 1. Lavrentiev Variational Principle and Auxiliary Transformations.
Chapter 2. RT-Algorithm for Conformal Mapping of an Arbitrary Fomain onto the Unit Circle and of a Doubly Connected Domain onto the Circular Annulus.
Chapter 3. Exterior Problems of Hydrodynamics.
Chapter 4. Interior Problems of Hydrodynamics.
Chapter 5. Liquid Sloshing in Cavities.
Conclusions.
Bibliography
Index
