1. Andrew Pendergast Comp 50H Final Project Presentation
Partial Differential Equation Modeling with FEniCS and Potential Applications in Chemistry
Andrew Pendergast
Comp 50H Final Project Presentation

2. Dynamical Systems Objects describing behavior changing over time
Function in terms of the partial derivatives (ex d/dx, d/dy, d/dt)
Integral in physics, mathematics, chemistry, and other applied sciences
Predicting and modeling complex behavior

3. Motivations and Background
PDE modeling as method for analyzing complex mathematical relationships
Systems composed of different compounds, media, forces, etc
Chromatography and Diffusion
van Deemter equation
Capillary columns and Packed columns
Why chromatography?

4. Method: FeNics Python Library
PDE solving library
Goal of developing scientific models from data and equations
Python with Anaconda
Functionality:
Given vector fields, functions, and parameterization of equations to find relationship between partial derivatives and distinct parent function of interest

5. Method: Coding with Fenics
1. Definition of mesh region representing domain of interest for u(x,t)
II. Definition of function space
III. Definition of boundary cases and initial value of a function
IV. Multiplication of initial value by vector field mesh
V. Utilization of methods to find solutions such that A == L == bc == u
VI. Analysis in Paraview

6. Demo: Gaussian and van deemter
Spyder, Fenics, Paraview

7. Future applications Data driven PDE modeling of diffusion
Direct partial behavior of each component compared to theoretical
Formalized differential equation knowledge
Expansion of van Deemter equation example beyond ‘B’ term