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.

Teachers

Johan Hoffman

Johan Jansson

Niclas Jansson

Literature

TBA

Lab modules

Lab 1: Vector spaces and linear transformations

Lab 2: Linear systems of equations

Lab 3: Nonlinear systems of equations

Lab 4: Function approximation

Lab 5: ODE

Lab 6: PDE I

Lab 7: PDE II

Lab 8: Optimization

Week plan

Week 1: Vector spaces and linear transformations 

• Lecture 1: Vector spaces
• Lecture 2: Linear transformations
• Lab 1

Week 2: Linear systems of equations

• Lecture 3: Linear systems of equations - Direct methods
• Lecture 4: Eigenvalue problems 
• Lab 2

Week 3: Nonlinear systems of equations

• Lecture 5: Linear system of equations - Iterative methods 
• Lecture 6: Nonlinear equations
• Lab 3

Week 4: ODE

• Lecture 7: ODE - time stepping/quadrature in 1D
• Lecture 8: ODE models
• Lab 4

Week 4: Function approximation

• Lecture 9: Function approximation - piecewise polynomials, LS/L2-projection
• Lecture 10: Quadrature in 2D/3D - mesh, reference element, quadrature, assembly  
• Lab 5

Week 6: PDE

• Lecture 11: 
• Lecture 12
• Lab 6

Week 7: PDE

• Lecture 13
• Lecture 14
• Lab 7

Week 8: Optimization

• Lecture 15
• Lecture 16
• Lab 8

Week 9

Written exam