Advances in the Complex Variable Boundary Element Method

Since its inception by Hromadka and Guymon in 1983, the Complex Variable Boundary Element Method or CVBEM has been the subject of several theoretical adventures as well as numerous exciting applications. The CVBEM is a numerical application of the Cauchy Integral theorem (well-known to students of complex variables) to two-dimensional potential problems involving the Laplace or Poisson equations. Because the numerical application is analytic, the approximation exactly solves the Laplace equation. This attribute of the CVBEM is a distinct advantage over other numerical techniques that develop only an inexact approximation of the Laplace equation. In this book, several of the advances in CVBEM technology, that have evolved since 1983, are assembled according to primary topics including theoretical developments, applications, and CVBEM modeling error analysis. The book is self-contained on a chapter basis so that the reader can go to the chapter of interest rather than necessarily reading the entire prior material. Most of the applications presented in this book are based on the computer programs listed in the prior CVBEM book published by Springer-Verlag (Hromadka and Lai, 1987) and so are not republished here.

Dr Hromadka is highly qualified in engineering and mathematics and has won several awards in both He has been involved with the CVBEM for years An essential text for anyone interested in this field * Both theory and practical applications are considered at length, making the topic easier to understand

Inhalt
Overview of the CVBEM.- Advanced CVBEM Topics; Variable/High Order Basis Functions; Multiply Connected Domains/Regions; Two Dimensional Problems.- Applications of the CVBEM in Mathematics, Science and Engineering; Computer Interaction; Groundwater Containment Transport; Geothernal Models; Freezing Fronts; Numerical Errors - Domain Heat Transport Models; Ice Segregation; Slow-Moving Interface Problems; Parabolic Equations.- Topics of Numerical Analysis; Expansion Using Fractals; Matrix System; Logarithms.- Numerical Error Analysis; Partial Differential Equations; Error Analysis; Collocation Points; Locating / Relative Error.- Appendix A.- Appendix B.- Author Index.- Index.