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Unit 0: Introduction and OpenMP programming

LectureDateTopics & videosHandouts
1Jan 25Course logistics
Introduction: root-finding methods		Logistics
Unit 0 slides
Root-finding notes
2Jan 27General performance model
C++ introduction
3Feb 1OpenMP programming

Unit 1: Advanced ODE integration methods

LectureDateTopics & videosHandouts
4Feb 3Runge–Kutta methods
Low-order Runge–Kutta methods		Unit 1 slides
Order condition notes
Symplectic methods
5Feb 8Order conditions
6Feb 10Practical error estimation
Dense output
–Feb 15Presidents' Day
7Feb 17Extrapolation methods
8Feb 22ODE stiffness

Unit 2: Advanced numerical linear algebra

LectureDateTopics & videosHandouts
9Feb 24BLAS & LAPACKUnit 2 slides
–Mar 1Wellness day
10Mar 3Krylov methods and preconditioning
11Mar 8Fast Fourier transform
Spectral methods
12Mar 10Domain decomposition

Unit 3: Finite element methods

LectureDateTopics & videosHandouts
–Mar 15No lectureFinal project slides
Unit 3 slides
FE example notes
13Mar 17Final project organization
Introduction
Variational formulation
14Mar 22Ritz–Galerkin methods
Function spaces
15Mar 24FEM boundary conditions
Finite element example
16Mar 29Standard finite elements

Unit 4: Finite volume methods

LectureDateTopics & videosHandouts
–Mar 31Wellness dayUnit 4 slides
17Apr 5Introduction
Multi-component systems
18Apr 7Riemann problem
Godunov method
Lax–Wendroff method
19Apr 12High-resolution methods
Limiters
20Apr 14Nonlinear equations and shocks

Unit 5: Special topics in scientific computing

LectureDateTopics & videosHandouts
21Apr 19Projection method for fluid mechanicsUnit 5 slides
22Apr 21Fluid simulation example
23Apr 26Level set method
Fast marching method
Barnes–Hut algorithm
–Apr 28No lecture