** The courses that are taught by Professor Gibou are (UCSB students are invited to consult individual course webpages on Gauchspace):**

### Level Set Methods (ME216, CS216, ECE226, ChemE226):

### Mathematics of Engineering (ME17):

### Numerical Analysis in Engineering (ME140A):

### Theoretical Analysis in Mechanical Engineering (ME140B):

### Introduction to Scientific Computing (CS111):

### Parallel Scientific Computing (CS140):

### Partial Differential Equations - Finite Difference Methods (ME210C, CS210C, ChemE210C):

The level set method is a general technique to keep track of a moving boundary that can undergo complex topological changes such as the merging and the breaking of complex flows. Since its introduction by Osher and Sethian in 1987 it has received considerable attention and applications have ranged from traditional fluid dynamics to materials science, computer vision and computer graphics.

In this course, students will review and learn mathematical techniques necessary for success as an engineer, both in future coursework and on the job. Given the difficulty of solving most realistic engineering problems analytically, the emphasis will be on the understanding and use of computational algorithms. In the process, students will develop a strong working knowledge of Matlab, which is an integrated technical computing environment that combines numeric computation, advanced graphics and visualization, and a high-level programming language. Topics include Ordinary Differential Equations, Partial Differential Equations, Eigenvalue Problems and Analysis of Experimental Data.

Numerical analysis and analytical solutions of problems described by linear and nonlinear differential equations with an emphasis on MATLAB. First and second order differential equations; systems of differential equations; linear algebraic equations, matrices and eigenvalues; boundary value problems; finite differences.

The goal for the class is for the students to learn and master the following: Derivation of Conservation Laws (Advection – Diffusion – Laplace – Burgers) - Classification of PDEs and their properties - Difference between linear .vs. nonlinear, homogeneous .vs. nonhomogeneous - Method of Separation of Variables & Fourier Series - Method of Characteristics - Numerical Methods for Hyperbolic, Parabolic, and Elliptic PDEs - Stability and Consistency Analysis. If time permits, Nonlinear Phenomena (shock waves and rarefaction waves).

This course is an introduction to scientific computing. Students will review and learn mathematical techniques necessary for simulating physical phenomena (ODEs and PDEs). Student will also apply this knowledge to Graphics applications as well as computer vision.

Fundamentals of high performance computing and parallel algorithm design for numerical computation. Topics include parallel architectures and clusters, parallel programming with message-passing libraries and threads, program parallelization methodologies, parallel performance evaluation and optimization, parallel numerical algorithms and applications with different performance tradeoffs.

Finite difference methods for hyperbolic, parabolic and elliptic PDE's, with application to problems in science and engineering. Convergence, consistency, order and stability of finite difference methods. Dissipation and dispersion. Finite volume methods. Software design and adaptivity.