Contemporary theory and practice in advanced scientific computation, organized by physical application area. Course comprises two 5-week modules, selected from the following:
Computational Fluid Dynamics: This module covers four basic contemporary issues: (i) the inherent nonlinearity of fluids; (ii) the mixed hyperbolic/elliptic nature of the differential equations governing fluid motion; (iii) the concomitant algorithmic complexity of their numerical treatment; and (iv) the size, i.e., the large number of degrees of freedom found in most realistic problems. Discussion of advection-dominated flows: physical and numerical properties; temporal and spatial discretization issues; method of characteristics, upwinding, Galerkin and Petrov-Galerkin methods; artificial viscosity. Navier-Stokes and shallow water equations in 2- and 3-D: mixed interpolation; primitive equation and higher-order formulation; staggered meshes; boundary conditions on pressure, transport and stress; radiation conditions. Frequency domain solution of hyperbolic problems: nonlinear generation of harmonics; truncation errors in iterative methods.
Prerequisites: ENGS 34 and ENGS 105, or equivalent
Computational Solid Mechanics: This module will deal with the development and application of finite element methods for solid mechanics problems. After a brief treatment of the theory of elasticity, the finite element equations for elastic solids will be developed using variational techniques. Applications in two- and three-dimensional static elasticity will be considered. Techniques will then be developed to analyze the following classes of problems; nonlinear material behavior, especially plasticity; plates and shells; problems involving contact between two bodies; and dynamic analysis of elastic bodies.
Prerequisites: ENGS 33 and ENGS 105, or equivalent
Computational Electromagnetics: This module focuses on numerical solutions of the Maxwell equations. Emphasis will be placed on problem formulation and implementation issues. Examples will be selected from a broad spectrum of topics such as electromagnetic scattering, waveguides, microwave circuits and strip-lines, bioelectromagnetics. Development of software to solve representative problems will be required. It is anticipated that the student will be capable of reading and understanding the current computational electromagnetics literature upon completion of this course.
Prerequisites: ENGS 105 and ENGS 120