Teacher : Alexey Shcherbakov (ITMO University – St Petersburg)

This lecture covers the following topics:

• Elements of the complexity theory and algorithms. Fast Fourier Transform and related topics.
• Selected topics of the matrix analysis. Krylov subspace methods for solution of large linear algebraic equation systems and eigenvalue problems.
• Fast algorithms for special type matrices and applications in the volume integral methods and the coupled dipole approximation. Spectra of nanoparticle aggregations.
• Sparse matrices and their application in the finite-difference and finite element methods.
• Calculation and analysis of band diagrams and dispersion curves, and overview of related physical phenomena.
• Advanced numerical integration and differentiation.
• Methods of solution to the 1D arbitrary potential tunneling problem. Anderson localization.
• Resonances in physical systems. Fano resonances in nanooptics. Perfect optical absorbers.
• Surface integral methods in the wave diffraction and scattering theory. Enhancement of local electromagnetic fields.
• Modal methods. Mie theory and Waterman T-matrix. Multiple scattering.
• Overview of the effective medium approximations in optics. Analytic results and numerical approaches.