# Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies

• Alexander G. Ramm
Book

1. Front Matter
Pages i-xii
2. Alexander G. Ramm
Pages 1-3
3. Alexander G. Ramm
Pages 5-14
4. Alexander G. Ramm
Pages 15-23
5. Alexander G. Ramm
Pages 25-39
6. Alexander G. Ramm
Pages 41-48
7. Alexander G. Ramm
Pages 49-62
8. Alexander G. Ramm
Pages 63-84
9. Alexander G. Ramm
Pages 85-112
10. Back Matter
Pages 117-122

### Introduction

Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var­ ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad­ vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal­ culation of multiple integrals. Of special interest is the case of inte­ grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.

### Keywords

Elektrostatik Fields Iteration Randwertproblem Streuung Wave Welle electromagnetic wave equation

#### Authors and affiliations

• Alexander G. Ramm
• 1
1. 1.Department of MathematicsKansas State UniversityManhattanUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-5715-8
• Copyright Information Springer-Verlag New York 1982
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-90682-9
• Online ISBN 978-1-4612-5715-8