Methods in Scientific Computing (DD2365), 7.5hp, Spring 2017

Course goals The goal of the course is to present general and efficient numerical methods and algorithms for basic models of computational science, in particular particle models, ordinary differential equations (ODE) and partial differential equations (PDE). Research challenges in the field are highlighted, e.g. with respect to parallel and distributed computing.

Course content
* 16 lectures
* 8 laboratory sessions
Examination
* Laboratory assignments Lab1-Lab6, 3.0p (P/F)
* Written examination, 4.5p (Grade: A, B, C, D, E, FX, F)
Teachers Johan HoffmanOffice hours: Tuesdays 9:00-10:00 (Office 4432, Lindstedtsvägen 5)

Johan Jansson

Niclas Jansson

Tania Bakhos

Van Dang Nguyen

Literature Lecture notes that are based in large parts on the following books.

[LIN] Trefethen, Bau, "Numerical Linear Algebra", SIAM, (ISBN 978-0-898713-61-9) [SIAM]

[CDE] Eriksson, Estep, Hansbo, Johnson, "Computational Differential Equations", Studentlitteratur, (ISBN 91-44-49311-8), 1996. [Bokus] [Studentlitteratur] [Kårbokhandeln]

NOTE: In some electronic versions of the CDE book, the Chapter 13 "Calculus of Several Variables" may be missing. For the problem sets the correct chapters should be: Chapter 8 "Two-Point Boundary Value Problems", Chapter 15: "The Poisson Equation", Chapter 21: "The Power of Abstraction".

Lab modules Lab1: Iterative methods for solving linear systems Lab2: ODE time stepping Lab3: FEM assembly Lab4: PDE and FEM in 1D/2D Lab5: Adaptive FEM Lab6: Optimization

Week plan Week 1
* Lecture 1: Vector spaces[Lecture notes 1]
* Lecture 2: Matrix algebra
* Lecture 3: Linear systems of equations - direct methods
Week 2
* Lecture 4: Eigenvalues and eigenvectors
* Lecture 5: Iterative methods
* Lab 1: Iterative methods for solving linear systems
Week 3
* Lecture 6: Nonlinear equations - Newton method
* Lecture 7: ODE - time stepping/quadrature in 1D
* Lab 2: ODE time stepping
Week 4
* Lecture 8: ODE models
* Lecture 9: Function approximation - piecewise polynomials, interpolation, LS/L2-projection
* Lecture 10: Quadrature in 2D/3D - quadrature, mesh, reference element, assembly algorithm
Week 5
* Lecture 11: PDE - FEM for 1D BVP model problems
* Lecture 12: PDE - FEM for 2D/3D BVP model problems
* Lecture 13: PDE - semi-discretization of PDE IVP
Week 6
* Lecture 14: Optimization - Adaptive FEM
* Lecture 15: Optimization - PDE constrained optimization
* Lecture 16: Course review
Week 7
* Lab 3: FEM Assembly
* Lab 4: PDE and FEM in 1D/2D
* Lab 5: Adaptive FEM
Week 8
* Lab 6: Optimization
* Lab 7: Lab review
* Lab 8: Lab review
Week 9 Written exam