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Lecture in WS 2015/16:
Numerical Analysis of Acoustic and Electromagnetic Scattering Problems (V5E4)
DateTuesday 12(c.t.)â€“14, Wegelerstr. 6, SR 6.020 (first lecture on 20. October 2015)
ContentWave phenomena in acoustics or electromagnetism are usually described by partial differential equations (PDEs), with the Helmholtz equation and Maxwell's equations being their most prominent instances. The inverse scattering problem considers the far-field pattern of an incoming wave to determine the position and the shape of unknown objects in a medium. Numerical simulations of these wave phenomena typically rely on spatial discretizaions with the finite element method.
After a short introduction to the physical modelling of the underlying equations, the course will introduce finite elements for time-harmonic wave propagation and analyze their stability and convergence properties. Furthermore, we will study selected topics of numerical inverse scattering.
The lecture will discuss the mathematics that underlies the numerical methods as well as their practical implementation. There will be an optional Practical Lab Numerical Simulation (P4E1) (→Basis link).
RequirementsContents of Modules Algorithmische Mathematik I/II, Einführung in die Grundlagen der Numerik and Wissenschaftliches Rechnen I as well as basic knowledge of finite element methods and functional analysis.
- D. Colton and R. Kress. Inverse acoustic and electromagnetic scattering theory ,volume 93 of Applied Mathematical Sciences. Springer, New York, third edition, 2013.
- F. Ihlenburg. Finite element analysis of acoustic scattering, volume 132 of Applied Mathematical Sciences. Springer-Verlag, New York, 1998.