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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
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 - Newton method
- 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: PDE - model problem in 1D
- Lecture 12: PDE - model problem in 2D/3D
- Lab 6
Week 7: PDE
- Lecture 13: PDE models
- Lecture 14: Time dependent PDE
- Lab 7
Week 8: Optimization
- Lecture 15
- Lecture 16
- Lab 8
Week 9
Written exam