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
Week 2
* Lecture 4: Eigenvalue problems
* Lab 2
Week 3: Nonlinear systems of equations
* Lecture 5: Linear system of equations - Iterative methodsecture 5: Iterative methods - Krylov methods
* Lab 1: Krylov methods
Week 3
* Lecture 6: Nonlinear equations - Newton method
* Lab 3
Week 4: ODE
* Lecture 7: ODE - tTime stepping/quadrature in 1D
* Lecture 8: ODE models
* Lab 4
Week 4: Function approximation ab 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 - Quadrature, mesh, reference element, quadrature, assembly
* Lab 5
Week 6: PDEassembly
Week 4
* Lecture 11: PDE - 1D BVP model problem in 1Ds
* Lecture 12: PDE - 2D/3D BVP model problem in 2D/3D
* Lab 6s
* Lecture 13: PDE - IVP PDE, semi discretization
Week 7: PDE6
* Lecture 134: PDE models
* Lecture 14: Time dependent PDE
* Lab 7
Week 8Optimization - 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
* Lecture 15
* Lecture 16
* Lab 8ab 7: Lab review
* Lab 8: Lab review
Week 9 Written exam