Instructor: Prof. Wei Cai, USTC 大师讲席教授 & UNC Charlotte, USA
Goal of the course: Introduce state-of-arts numerical methods in computational physics for applications in biology, nano-optics, electromagnetic wave scattering, electron transport in plasma and semi-conductors.
Audience：Graduate students and senior undergraduates, from areas in applied/computational mathematics, applied physics, optics, plasma physics, mesoscopic material science, electric circuits, microwave and quantum devices, with research interest in scientific and engineering computing.
Hours of lectures: total 45-50 one hour lectures, 2013/11/29-2014/1/11, 6 hours per week
Mon.（3、4）5205；Wed.（3、4）5107；Fri.（3、4）5107
Textbook: Wei Cai, Computational Methods for Electromagnetic Phenomena: Electrostatics in solvation, scattering, and electron transport, Cambridge University Press, 2013.
The following numerical methods will be covered in this class:
1. Statistical fluctuation formulae for dielectric constants and molecular dynamic simulations for biological systems
2. Particle mesh Ewald (PME), Fast multipole method (FMM), and image-based reaction field methods for long-range interactions
3. High-order singular/hyper-singular (Nystrom /Galerkin) boundary and volume integral methods in layered media for (a) Debye�Huckel theory & Poisson�Boltzmann electrostatics, (b) electromagnetic scattering, and (c) electron waves in quantum dots
4. Absorbing and UPML boundary conditions for electromagnetic (EM) wave scatterings
5. High-order hierarchical Nedelec edge elements for Maxwell equations
6. High-order discontinuous Galerkin (DG) and Yee scheme methods for EM waves
7. Finite element and plane wave frequency-domain methods for periodic structures/surface plasmons, and Bloch wave expansions and photonic bandgap calculation
8. High-order WENO, Godunov and central schemes for hydrodynamic Transport in semiconductor devices
9. Vlasov�Fokker�Planck, Particle-in-cell (PIC), and constrained MHD transport in plasmas
欢迎感兴趣的师生参加！
中国科学技术大学数学科学学院
