Math 270 A: Techniques of Scientific Computing

Math 270 A: Techniques in Scientific Computing
MS 6229, MWF, 2-2:50 PM
Professor: Joseph Teran
Office: MS 2619E
Office hours: MW, 3-4
Overview

We will focus on techniques from scientific computing related to computational solid and fluid dynamics. Numerical methods for hyperbolic, parabolic and elliptic partial differential equations will be investigated in the broader context of the inviscid Euler equations, Navier-Stokes equations, Stokes equations and static/dynamic equations of hyperelastic solids. Emphasis will be on implementation of popular numerical methods for computational solids and fluids.

Schedule

Week 1: Basic Continuum Mechanics: Inviscid Euler, Navier Stokes and Stokes Equations
Week 2: Projection Methods, Poisson Equations and Multigrid, Part 1
Week 3: Projection Methods, Poisson Equations and Multigrid, Part 2
Week 4: The Heat Equation and Implicit Time Stepping
Week 5: Stokes/Navier Stokes Implementation Details
Week 6: Basic Continuum Mechanics: Dynamic and Static Hyperelasticity
Week 7: Linear Elasticity
Week 8: Finite Element Methods
Week 9: Incompressibility
Week 10: Nonlinear Elasticity: St. Venant-Kerchoff, Neo-Hookean and Mooney-Rivlin Materials

Assignments

Comments

We are more or less done with continuum mechanics, but a helpful reference is: A First Course in Continuum Mechanics by Oscar Gonzalez and Andrew Stuart.
McCormack reference: Selle, A., Fedkiw, R., B.-M Kim, Y. Liu, and J. Rossignac, "An Unconditionally Stable MacCormack Method", J. Sci. Comput. 35, 350-371 (2008).
My MG, algebra, and grid classes.
My frame and movie visualization files.