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

Tania Bakhos ¶

Van Dang Nguyen ¶

Literature TBA

Lab modules Lab 1: Krylov methods Lab 2: ODE time stepping Lab 3: FEM assembly Lab 4: PDE/ and FEM in 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 - Ddirect 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 - Ttime stepping/quadrature in 1D
* Lab 2: ODE time stepping
Week 4
* Lecture 8: ODE models
* Lecture 9: Function approximation - Ppiecewise polynomials, interpolation, LS/L2-projection
* Lecture 10: Quadrature in 2D/3D - Qquadrature, 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 - IVP PDE, semi -discretization of PDE IVP
Week 6
* Lecture 14: Optimization - Adaptive FEM
* Lecture 15 Optimization - Optimal controlPDE constrained optimization
* Lecture 16: Course review
Week 7
* Lab 3: FEM Assembly
* Lab 4: FEMPDE 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