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: Krylov methods

Lab 2: ODE time stepping

Lab 3: FEM assembly

Lab 4: FEM 1D/2D

Lab 5: Adaptive FEM

Lab 6: Optimization

Week plan

Week 1 

• Lecture 1: Vector spaces
• Lecture 2: Linear transformations
• Lecture 3: Linear systems of equations - Direct methods

Week 2 

• Lecture 4: Eigenvalue problems 
• Lecture 5: Iterative methods - Krylov methods 
• Lab 1: Krylov methods

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  

Week 4 

• Lecture 11: PDE - 1D BVP model problems
• Lecture 12: PDE - 2D/3D BVP model problems
• Lecture 13: PDE - IVP PDE, semi discretization 

Week 6 

• Lecture 14: Optimization - Adaptive FEM
• Lecture 15 Optimization - Quadratic programming
• Lecture 16: Course review

Week 7 

• Lab 3: FEM Assembly
• Lab 4: FEM 1D/2D 
• Lab 5: Adaptive FEM

Week 8

• Lab 6: Optimization
• Lab 7: Lab review
• Lab 8: Lab review 

Week 9

Written exam