Computational methods for classical PDEs in the physical sciences (MATH-GA.2011-003, CSCI-GA 2945.003)
This special topics class in Numerical Analysis will be taught in-person Wednesdays 11:00-12:50PM in Warren Weaver Hall 512. It can be thought of as Numerical Methods III.
This seminar will follow up on Numerical Methods II and cover more advanced computational methods (finite difference (FD), volume (FV), and element (FE) schemes including boundary conditions, and boundary integral methods) for solving PDEs that arise in physical sciences. The class will assume familiarity with multi-step and multi-stage (Runge-Kutta) methods for solving systems of ODEs including stability theory, basic finite difference methods for elliptic, parabolic, and hyperbolic PDEs (including von Neumann/Fourier stability analysis), and basic spectral methods (e.g. FFT-based schemes for periodic domains). The class will cover electrostatics (FD and FEM for Poisson including geometric and algebraic multigrid, Laplace in confined domains using boundary integral), elasticity (variational formulation, finite-element methods), linear wave equation (electromagnetism, acoustics, geofluids), and fluid dynamics (FD/FV for 1D conservation laws including dispersion and dissipation, stability, accuracy, and modified equations, FV advection-diffusion including limiters, MAC/FEM for incompressible Navier-Stokes, immersed-boundary method, Stokes flow including boundary-integral methods).
The computational fluid dynamics portion of the class, which will be about one half or so, will be similar to that from my CFD class, so consult that if deciding whether to take this class.