# Numerical Methods in Computational Electrodynamics

## Linear Systems in Practical Applications

• Ursula van Rienen
Book

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 12)

1. Front Matter
Pages I-XIII
2. Ursula van Rienen
Pages 1-9
3. Ursula van Rienen
Pages 11-34
4. Ursula van Rienen
Pages 35-81
5. Ursula van Rienen
Pages 83-203
6. Ursula van Rienen
Pages 205-241
7. Ursula van Rienen
Pages 243-333
8. Ursula van Rienen
Pages 335-336
9. Back Matter
Pages 337-379

### Introduction

treated in more detail. They are just specimen of larger classes of schemes. Es­ sentially, we have to distinguish between semi-analytical methods, discretiza­ tion methods, and lumped circuit models. The semi-analytical methods and the discretization methods start directly from Maxwell's equations. Semi-analytical methods are concentrated on the analytical level: They use a computer only to evaluate expressions and to solve resulting linear algebraic problems. The best known semi-analytical methods are the mode matching method, which is described in subsection 2. 1, the method of integral equations, and the method of moments. In the method of integral equations, the given boundary value problem is transformed into an integral equation with the aid of a suitable Greens' function. In the method of moments, which includes the mode matching method as a special case, the solution function is represented by a linear combination of appropriately weighted basis func­ tions. The treatment of complex geometrical structures is very difficult for these methods or only possible after geometric simplifications: In the method of integral equations, the Greens function has to satisfy the boundary condi­ tions. In the mode matching method, it must be possible to decompose the domain into subdomains in which the problem can be solved analytically, thus allowing to find the basis functions. Nevertheless, there are some ap­ plications for which the semi-analytic methods are the best suited solution methods. For example, an application from accelerator physics used the mode matching technique (see subsection 5. 4).

### Keywords

Beschleunigerphysik Elektrotechnik und Informationstechnik HTS accelerator physic algorithm comput mathematics numerical methods simulation

#### Authors and affiliations

• Ursula van Rienen
• 1
1. 1.Fachbereich Elektrotechnik und InformationstechnikUniversität RostockRostockGermany

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-642-56802-2
• Copyright Information Springer-Verlag Berlin Heidelberg 2001
• Publisher Name Springer, Berlin, Heidelberg
• eBook Packages
• Print ISBN 978-3-540-67629-4
• Online ISBN 978-3-642-56802-2
• Series Print ISSN 1439-7358
• Buy this book on publisher's site