**Hari Sundar**

🏢 3454 MEB ☎ 801-585-9913 ✉ hari@cs.utah.edu

Office hours: Tue 2-4pm, MEB 3454

Lecture: Tu,Th 9:10-10:30 Teaching Assistant: Arnab Das

Our primary goal would be to solve partial differential equations numerically. This course will focus heavily on the math and numerics, but you will be expected to implement the methods we cover in a language of your choice. Good options are high-level languages with strong linear algebra support/libraries such as Matlab (Links to an external site.)Links to an external site., Julia (Links to an external site.)Links to an external site. or Python with NumPy/SciPy. Familiarity with at least one of these is strongly recommended.

**Prerequisite:** Adv. Scientific Computing I or a graduate-level linear algebra course plus good understanding of ordinary differential equations.
Course Organization

**Lectures.** We will meet for lecture twice a week for 80 minutes. I will use a combination of a laptop and a (digital) whiteboard during lectures. I will use the laptop to present programming examples and perform demonstrations; I also make use of slides. I will make the laptop-based examples available online, but you will need to take notes if you want to keep track of what I write on the board or say out loud.

There is no substitute for attending lectures; I expect all students to attend all lectures. You will not be able to completely reconstruct lectures after the fact from the slides and examples that I post online. There is no substitute for participating actively in lecture; I expect all students to put away their electronic devices and pay attention. You may think you’re good at multi-tasking, but I disagree.

There is no formal textbook for this course. I will post notes on canvas, but please note that this is not a replacement for what we cover in class.

These will be up to 6 homework assignments that are a combination of math and programming problems. The problems are set as practical problems that you will first work the math out for and then implement to solve the problem numerically. All assignments are worth 100 points and your final grade will be determined based on your average score across all assignments. We will not be having any exams in this course. Cooperation vs. Cheating

Working with others on assignments is a good way to learn the material and we encourage it. However,there are limits to the degree of cooperation that we will permit. When taking an online quiz or an in-class exam, you must work completely independently of everyone else. Any collaboration here, of course, is cheating.

You must limit your discussions with other students of programs or written assignments to a high-level discussion of solution strategies. If you do collaborate with other students in this way, the solution that you submit must identify the students and describe the nature of the collaboration. The solution that you hand in for programs or written assignments must be written in your own words. If you base your solution on any other written solution, regardless of the source, you are cheating.

We do not distinguish between cheaters who copy others’ work and cheaters who allow their work to be copied.

If you have any questions about what constitutes cheating, please ask.

If you cheat, you will be given an E in the course and your case will be handled as detailed here (Links to an external site.)Links to an external site..

In addition, please remember to read the College (Links to an external site.)Links to an external site. and Department (Links to an external site.)Links to an external site. guidelines. Students with Disabilities

Reasonable accommodation will gladly be provided to the known disabilities of students in the class. Please let the instructor know of such situations as soon as possible. If you wish to qualify for exemptions under the Americans With Disabilities Act (ADA), you should also notify the Center for Disabled Students Services, 160 Union Building.

- Numerical Methods for Partial Differential Equations (Intro, Fourier Analysis)
- Finite Difference Discretization
- Elliptic Equations
- 1D Problem
- FD Formulas and Multidimensional Problems

- Parabolic Problems

- Elliptic Equations
- Solution Methods
- Iterative Techniques
- Multigrid Techniques
- Direct Solvers (6210?)

- Hyperbolic Equations
- Finite Difference Discretization of Hyperbolic Equations: Linear Problems
- Scalar One-Dimensional Conservation Laws
- Numerical Schemes for Scalar One-Dimensional Conservation Laws

- Finite Element Methods for Elliptic Problems
- Variational Formulation: The Poisson Problem
- Discretization of the Poisson Problem in R1
- Formulation
- Theory and Implementation -The Poisson Problem in R2Finite Element Methods for Elliptic Problems

- Integral Equation Methods
- Discretization of Boundary Integral Equations
- Numerical Quadrature
- Discretization Convergence Theory
- Formulating Boundary Integral Equations
- First and Second Kind Potential Equations

- PDE Constrained Optimization
- Lagrange Multipliers
- First Order Optimality, KKT Conditions
- Regularization