401-3640-70L  Volume Integral Equations: Theory and Numerics

SemesterHerbstsemester 2020
DozierendeR. Hiptmair
Periodizitäteinmalige Veranstaltung
KommentarNumber of participants limited to 10.

KurzbeschreibungThe seminar covers recent research articles on the theory and numerical treatment of volume integral equations for acoustic and electromagnetic scattering problems.
LernzielBeside conveying knowledge about the functional analytic method for analyzing integral equations and a range of numerical methods, the seminar is also meant to practise scientific presentation skills.
InhaltTopics (based on research articles)
1. VIE for acoustic scattering
2.The Operator Equations of Lippmann-Schwinger Type for Acoustic and Elec-
tromagnetic Scattering Problems in L2
3. VIE for electromagnetic scattering at dielectric bodies
4. Fast Solvers for the Lippmann-Schwinger equation
5. Numerical Solution of the Lippmann–Schwinger Equation by “Approx-
imate Approximations”
6. Higher-order Fourier approximation in scattering by two-dimensional, inho-
mogeneous media
7. Fast convolution with free-space Green’s functions
8. Fast numerical solution of the electromagnetic medium scattering problem
9. VIE Methods for Time-Harmonic Solutions of Maxwell’s Equations: Discretization, Spectrum and Preconditioning
10. The Discrete Dipole Approximation: an overview and recent developments