GEO 391: Computational Methods for Geophysics Unique number: 27075 Instructor: Omar Ghattas (omar@ices.utexas.edu; www.cs.cmu.edu/~oghattas) Meeting time: Tues/Thur 2:00-4:00pm (may change to accomodate students' schedules) Location: GEO 3.120 Description: This course treats numerical methods for the solution of partial differential equations arising in continuum geophysics and geodynamics. Our focus is on finite element methods, for their generality and adaptivity. We will develop the core ingredients of the method -- weak formulation, Galerkin approximation, piecewise polynomial basis functions, numerical quadrature, isoparametric elements, assembly, sparse solvers -- with reference to a model potential problem. We will then extend the ideas to problems in heat conduction and viscous flow (mantle convection), elastodynamics (seismic wave propagation), and porous media flow and transport. We will use a high-level toolkit (deal.II) to build simulators in each of these areas. The course will be relatively self-contained. The background required is just the mathematics in an undergraduate science or engineering curriculum -- vector calculus, linear algebra, and differential equations.