文档介绍：TEL AVIV UNIVERSITY
The Raymond and Beverly Sackler Faculty of Exact Sciences
School of Mathematical Sciences
HIGH-ORDER ACCURATE METHODS
FOR MAXWELL EQUATIONS
Thesis submitted for the degree “Doctor of Philosophy”
by
Eugene Kashdan
Submitted to the senate of Tel Aviv University
June 2004
This work was carried out under the supervision of
Professor Eli Turkel
Acknowledgements
I would like to express my gratitude and deepest appreciation to Professor Eli
Turkel for his guidance, counseling and for his friendship. Without his help and
encouragement this work would never have been done.
I wish to thank my parents and my sister Maya for their love, support and belief in
my ess, in spite of the thousands of kilometers between us.
I would like to thank my colleagues at Tel Aviv University for their great help,
friendship and hours of the scientific (and not too much scientific) discussions.
I should also mention that my PhD research was supported by the Israeli Ministry
of Science with the Eshkol Fellowship for Strategic Research in years
2000 – 2002 and supported in part by the Absorption Foundation ("Keren Klita") of Tel
Aviv University all other years.
Finally, I would like to acknowledge the use puter resources belonging to
the High puting Unit, a division of the Inter puting
Center, which is a consortium formed by research universities in Israel.
Contents
1 Introduction 1
2 Preliminaries 6
Physical background . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Maxwell equations in various coordinate systems . . . . . . . . . . . . 8
Cartesian coordinates . . . . . . . . . . . . . . . . . . . . . . . 8
Cylindrical coordinates . . . . . . . . . . . . . . . . . . . . . . 9
Spherical coordinates . . . . . . . . . . . . . . . . . . . . . . . 9
3 Boundary c