## AA 214A: Numerical Methods in Engineering and Applied Sciences (CME 207, GEOPHYS 217)

Scientific computing and numerical analysis for physical sciences and engineering. Advanced version of CME206 that, apart from CME206 material, includes nonlinear PDEs, multidimensional interpolation and integration and an extended discussion of stability for initial boundary value problems. Recommended for students who have some prior numerical analysis experience. Topics include: 1D and multi-D interpolation, numerical integration in 1D and multi-D including adaptive quadrature, numerical solutions of ordinary differential equations (ODEs) including stability, numerical solutions of 1D and multi-D linear and nonlinear partial differential equations (PDEs) including concepts of stability and accuracy. Prerequisites: linear algebra, introductory numerical analysis (
CME 108 or equivalent).

Terms: Aut
| Units: 3

## AA 214B: Numerical Methods for Compressible Flows

For M.S.-level graduate students. Covers the hierarchy of mathematical models for compressible flows. Introduction to finite difference, finite volume, and finite element methods for their computation. Ideal potential flow; transonic potential flow; Euler equations; Navier-Stokes equations; representative model problems; shocks, expansions, and contact discontinuities; treatment of boundary conditions; time and pseudo-time integration schemes. Prerequisites: basic knowledge of linear algebra and ODEs (
CME 206 or equivalent).

Terms: Win
| Units: 3

Instructors:
Farhat, C. (PI)
;
Boncoraglio, G. (TA)

## AA 214C: Numerical Computation of Viscous Flow

Numerical methods for solving parabolic sets of partial differential equations. Numerical approximation of the equations describing compressible viscous flow with adiabatic, isothermal, slip, and no-slip wall boundary conditions. Applications to the Navier-Stokes equations in two and three dimensions at high Reynolds number. Computational problems are assigned. Prerequisite: 214B.

Terms: Spr
| Units: 3

Instructors:
Jameson, A. (PI)

## AA 215A: Advanced Computational Fluid Dynamics (CME 215A)

High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.

Terms: Win
| Units: 3

Instructors:
Jameson, A. (PI)

## AA 215B: Advanced Computational Fluid Dynamics (CME 215B)

High resolution schemes for capturing shock waves and contact discontinuities; upwinding and artificial diffusion; LED and TVD concepts; alternative flow splittings; numerical shock structure. Discretization of Euler and Navier Stokes equations on unstructured meshes; the relationship between finite volume and finite element methods. Time discretization; explicit and implicit schemes; acceleration of steady state calculations; residual averaging; math grid preconditioning. Automatic design; inverse problems and aerodynamic shape optimization via adjoint methods. Pre- or corequisite: 214B or equivalent.

Last offered: Spring 2012

## AA 218: Introduction to Symmetry Analysis

Methods of symmetry analysis and their use in the reduction and simplification of physical problems. Topics: dimensional analysis, phase-space analysis of autonomous systems of ordinary differential equations, use of Lie groups to reduce the order of nonlinear ODEs and to generate integrating factors, use of Lie groups to reduce the dimension of partial differential equations and to generate similarity variables, exact solutions of nonlinear PDEs generated from groups. Mathematica-based software developed by the instructor is used for finding invariant groups of ODEs and PDEs.

Terms: Spr
| Units: 3

## AA 222: Introduction to Multidisciplinary Design Optimization (CS 361)

Design of engineering systems within a formal optimization framework. Engineering often involves the synthesis of several disciplines, such as fluids, structures, and controls in aerospace systems. These disciplines interact in complex ways, making the optimization of the system design challenging. This course covers the mathematical and algorithmic fundamentals of optimization, including derivative and derivative-free approaches for both linear and non-linear problems, with an emphasis on multidisciplinary design optimization. Topics will also include quantitative methodologies for addressing various challenges, such as accommodating multiple objectives, handling uncertainty in evaluations, selecting design points for experimentation, and principled methods for optimization when evaluations are expensive. Applications range from the design of aircraft to automated vehicles. Prerequisites: some familiarity with probability, programming, and multivariable calculus.

Terms: Spr
| Units: 3-4

## AA 228: Decision Making under Uncertainty (CS 238)

This course is designed to increase awareness and appreciation for why uncertainty matters, particularly for aerospace applications. Introduces decision making under uncertainty from a computational perspective and provides an overview of the necessary tools for building autonomous and decision-support systems. Following an introduction to probabilistic models and decision theory, the course will cover computational methods for solving decision problems with stochastic dynamics, model uncertainty, and imperfect state information. Topics include: Bayesian networks, influence diagrams, dynamic programming, reinforcement learning, and partially observable Markov decision processes. Applications cover: air traffic control, aviation surveillance systems, autonomous vehicles, and robotic planetary exploration. Prerequisites: basic probability and fluency in a high-level programming language.

Terms: Aut
| Units: 3-4

Instructors:
Kochenderfer, M. (PI)
;
Chan, E. (TA)
;
Morton, J. (TA)
...
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Instructors:
Kochenderfer, M. (PI)
;
Chan, E. (TA)
;
Morton, J. (TA)
;
Sunberg, Z. (TA)
;
Tompa, R. (TA)

## AA 229: Advanced Topics in Sequential Decision Making (CS 239)

Survey of recent research advances in intelligent decision making for dynamic environments from a computational perspective. Efficient algorithms for single and multiagent planning in situations where a model of the environment may or may not be known. Partially observable Markov decision processes, approximate dynamic programming, and reinforcement learning. New approaches for overcoming challenges in generalization from experience, exploration of the environment, and model representation so that these methods can scale to real problems in a variety of domains including aerospace, air traffic control, and robotics. Students are expected to produce an original research paper on a relevant topic. Prerequisites:
AA 228/
CS 238 or
CS 221.

Last offered: Winter 2016

## AA 236A: Spacecraft Design

The design of unmanned spacecraft and spacecraft subsystems emphasizing identification of design drivers and current design methods. Topics: spacecraft configuration design, mechanical design, structure and thermal subsystem design, attitude control, electric power, command and telemetry, and design integration and operations.

Terms: Aut
| Units: 3-5

Instructors:
Kalman, A. (PI)
;
Meginnis, A. (TA)

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