Partial differential equations: dimensional analysis, characteristic scales, special solutions, advection, diffusion, dispersion and diffraction, well-posedness and solution operator.
Methods of discretization: finite and compact finite differences, spectral and finite element methods, operator splitting and fractional steps.
Numerical boundary conditions: well-posedness, transparent and absorbing (PML) boundary conditions.
Problems with different time and space scales: resolve or not resolve, stiff and highly oscillatory solutions, singularities in the material, geometry and solutions, linear and nonlinear smoothing, limiters.
