Electromagnetic fields and waves: mathematical models and numerical methods
Larisa Beilina, Yury Shestopalov
Short description
The first part of this course gives a basic introduction to the mathematical foundations of the
electromagnetic and acoustic field theory. The second part of the course deals with new
numerical methods and efficient implementation of the Maxwell's system in the time-domain.
Location and Dates
Department of Mathematical Sciences, fall semester 2011.
Introductory lecture:
Thursday September 15, 10.00-11.45, MVL 14.
Aim of the course
After a successful completion of the course the students will be able to apply mathematical
methods for the analysis of the boundary value problems of the theory of wave diffraction and
propagation. Students will be also able to handle numerical methods (finite elements, finite
difference and domain decomposition methods) for solutions of the time-dependent Maxwell's
equations.
Target group
Graduate students in mathematics and physics.
Entry requirements
Basic undergraduate mathematics courses in calculus in several dimensions, vector analysis and partial
differential equations.
Course organizers
Larisa Beilina (larisa@chalmers.se)
Yuri Shestopalov (youri.shestopalov@kau.se)
Teaching staff
Larisa Beilina (larisa@chalmers.se)
Yuri Shestopalov (youri.shestopalov@kau.se)
Course program
Introduction to the basic electromagnetic theory. Maxwell's and Helmholz equations. Statement and
analysis of boundary value problems of the mathematical theory of wave diffraction and propagation in
guides. Introduction to the integral equations method. Variational principles for electromagnetics. Finite
element analysis in time domain. Finite element and finite difference methods for solutions of Maxwell's
equations. A posteriori error analysis and adaptive error control in the finite element approximation of
Maxwell's system.
Lectures
16 double hours.
Exam
Project work with an written report.
Registration
Please contact the course organizers for information.
Literature
A.N. Tikhonov, A.A. Samarskij, Equations of Mathematical Physics, Dover Publications, 1990. ISBN 0486-66422-8.
D. Colton and R. Kress, Integral Equation Methods in Scattering Theory, Wiley-Interscience
Publication, New York (1983).
D.
Colton and R. Kress, Inverse Acoustic and Electromagnetic Scattering Theory, Applied
Mathematical Sciences 93, Springer-Verlag, Heidelberg (1992), 2nd Edition, 1998.
DI.
J.Jin, The Finite Element Method in Electromagnetics, second edition. J.Wiley and sons, 2002.
P.B.Monk, Finite Element Methods for Maxwell's equations. Oxford university press, 2003.
G. Kristensson, Elektromagnetisk vågutbredning, Studentlitteratur, Lund, 1999.
S. Larsson, V. Thomée, Partial Differential Equations with Numerical Methods, Applied Mathematical
Sciences, Springer-Verlag, Heidelberg (2003).
A.Taflove, Advances in computational electromagnetics:the finite difference time-domain method.
Boston, M-house, 1998.