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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 - 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 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