Data Driven Modeling
&
Scientific Computation

Dimensionality Reduction for PDEs

Lecture 1: Ch. 19.1

 

Stacks Image 66994

 

[ view ]

 
BASIS SELECTION AND IDEAL MODES: This lecture provides an introduction to basis representations, POD modes, and orthogonality of function spaces.

 

MATLAB COMMANDS

FFT

Lecture 2: Ch. 19.2

 

Stacks Image 67009

 

[ view ]

 
SPECIAL FUNCTIONS + GALERKIN PROJECTIONS: The harmonic oscillator is considered along with its ideal basis functions: the Gauss-Hermite polynomials.

 

MATLAB COMMANDS

SVD

Lecture 3: Ch. 19.3

 

Stacks Image 67024

 

[ view ]

 
POD EXPANSION : We construct a ROM model of the nonlinear Schrodinger equation using a 2 POD mode expansion.

 

MATLAB COMMANDS

ODE45

© 2019 kutz