GG630: Numerical Modeling of Physical SystemsDescription: Text Box:

Tue/Thu 10:30-11:45

 

Instructors: Garrett Apuzen-Ito (gito@hawaii.edu, POST 810)

Prerequisites: Instructor consent.  Some experience with differential equations, vector calculus, linear algebra, as well as Matlab is needed.

Textbook: Numerical Methods for Engineers and Scientists, 2nd Edition, Joe D. Hoffman, Taylor & Francis Group

 

Overview and Objectives:

This course will introduce finite difference methods commonly used for solving ordinary differential equations (ODE’s) and partial differential equations (PDE’s) in Earth and planetary sciences.  You will learn how to turn a concept of a geologic phenomenon into a mathematical model, to solve the equations, and to verify the accuracy of the solutions.  You will leave the course with the foundation needed to evaluate modeling-based research by others as well as build your own simple geodynamic models.   

 

Format and workload

Tuesdays will be used primarily for lectures; Thursdays will be used for demonstrations and discussions of homework.  Homework will be assigned approximately weekly and will involve using Matlab to program and practice the techniques covered.  Besides building familiarity and know-how, the work produced will represent a diverse and powerful numerical toolbox for solving a variety of problems in geodynamics.  There will be no exams, but instead, the culminating experience will be a projects in which you form a numerical model of a geologic system of your own interest. The projects will include a short written report and a few class presentations.   

 

Course Outline

 

Part I Basic Tools of Numerical Analysis

•Differential Equations and Introduction to Modeling (Week 1)

•Numerical Techniques for Solving Nonlinear Equations, Ch. 3 (Week 2)

•Numerical Differentiation and Taylor Series, Ch. 5 (Week 3)

•Numerical Integration, Ch. 6, e.g., Newton-Cotes, Gauss Quadrature (Week 4)

 

Part II. Ordinary Differential Equations (ODE’s)

•Initial-Value ODE’s, Ch 7, e.g., Euler’s Method, Runge-Kutta (Week 5)

•Boundary-Value ODE’s, Ch 8, e.g., Equilibrium Methods (Week 6 and 7)

 

Part III. Partial Differential Equations (PDE’s)

•Elliptic PDE’s, e.g. Gauss-Seidel, SOR for solving Laplace’s Equation (Week 8 & 9)

•Parabolic PDE’s, e.g., explicit & implicit methods for solving non-steady diffusion (Weeks 10 & 11)

•Hyperbolic PDE’s, e.g., Lax-Wenthrop, particle-in-cell methods for solving advection (Weeks 12 & 13)