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

Last offered: Winter 2017

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

## CME 245: Topics in Mathematical and Computational Finance

Description: Current topics for enrolled students in the MCF program: This course is an introduction to computational, statistical, and optimizations methods and their application to financial markets. Class will consist of lectures and real-time problem solving. Topics: Python & R programming, interest rates, Black-Scholes model, financial time series, capital asset pricing model (CAPM), options, optimization methods, and machine learning algorithms. Appropriate for anyone with a technical and solid applied math background interested in honing skills in quantitative finance. Prerequisite: basic statistics and exposure to programming.Can be repeated up to three times.

Last offered: Summer 2017
| Repeatable for credit

## CME 253A: Introduction to High Performance Computing and Parallel (GPU) Computing

Introduction to high-performance-computing (HPC) for mathematical, computational, physical sciences and engineering within the field of computational fluid dynamics (CFD) and mechanics; particular focus on parallel computing using GPU accelerators and 3-D code development with application to nonlinear PDEs related to Earth science dynamical systems; evaluation of performance limiters and discussion on basic optimization techniques; finite-difference discretization (stencil codes) and accelerated iterative methods. Programming languages: MATLAB, CUDA C, (MPI). Hands-on approach: starting from diffusion and wave propagation physics, the goal being to achieve a 3-D Stokes flow utilizing C CUDA in order to leverage the GPU computing power. Pre-requisites: basic programming skills (e.g. MATLAB) and Scientific computing. Basic knowledge of compiled languages (C) and CFD are a plus.

Last offered: Summer 2019

## CME 258: Libraries for Numerical Linear Algebra and Optimization

This course will cover standard libraries commonly used for numerical linear algebra and optimization, with an emphasis on giving students experience with using the libraries on real examples. The course will cover software for direct methods (BLAS, Atlas, LAPACK, Eigen), iterative methods (ARPACK, Krylov Methods), and linear/nonlinear optimization (MINOS, SNOPT). Prerequisites: at least one course in numerical linear algebra (preferably at the level of
CME 200 or
CME 302), and one course in numerical optimization, as well as experience with at least one compiled language such as C/C++/Fortran.

Last offered: Spring 2018

## CME 321A: Mathematical Methods of Imaging (MATH 221A)

Image denoising and deblurring with optimization and partial differential equations methods. Imaging functionals based on total variation and l-1 minimization. Fast algorithms and their implementation.

Last offered: Winter 2014

## CME 345: Model Reduction

Model reduction is an indispensable tool for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control. This course presents the basic mathematical theory for projection-based model reduction. Topics include: notions of linear dynamical systems and projection; projection-based model reduction; error analysis; proper orthogonal decomposition; Hankel operator and balancing of a linear dynamical system; balanced truncation method: modal truncation and other reduction methods for linear oscillators; model reduction via moment matching methods based on Krylov subspaces; introduction to model reduction of parametric systems and notions of nonlinear model reduction. Course material is complemented by a balanced set of theoretical, algorithmic and Matlab computer programming assignments. Prerequisites:
CME 200 or equivalent,
CME 263 or equivalent and basic numerical methods for ODEs.

Last offered: Spring 2017

## CME 364A: Convex Optimization I (CS 334A, EE 364A)

Convex sets, functions, and optimization problems. The basics of convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications. Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming. Numerical algorithms for smooth and equality constrained problems; interior-point methods for inequality constrained problems. Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering. Prerequisite: linear algebra such as
EE263, basic probability.

Terms: Win, Sum
| Units: 3

Instructors:
Diamond, S. (PI)
;
Duchi, J. (PI)
;
Cauchois, M. (TA)
...
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Instructors:
Diamond, S. (PI)
;
Duchi, J. (PI)
;
Cauchois, M. (TA)
;
Fu, A. (TA)
;
Kim, J. (TA)
;
Luxenberg, E. (TA)
;
Marsden, A. (TA)

## CME 364B: Convex Optimization II (EE 364B)

Continuation of 364A. Subgradient, cutting-plane, and ellipsoid methods. Decentralized convex optimization via primal and dual decomposition. Monotone operators and proximal methods; alternating direction method of multipliers. Exploiting problem structure in implementation. Convex relaxations of hard problems. Global optimization via branch and bound. Robust and stochastic optimization. Applications in areas such as control, circuit design, signal processing, and communications. Course requirements include project. Prerequisite: 364A.

Terms: Spr
| Units: 3

Instructors:
Pilanci, M. (PI)

## CME 375: Advanced Topics in Convex Optimization (MATH 301)

Modern developments in convex optimization: semidefinite programming; novel and efficient first-order algorithms for smooth and nonsmooth convex optimization. Emphasis on numerical methods suitable for large scale problems arising in science and engineering. Prerequisites: convex optimization (
EE 364), linear algebra (
Math 104), numerical linear algebra (
CME 302); background in probability, statistics, real analysis and numerical optimization.

Last offered: Winter 2015
| Repeatable for credit

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