Ändringar mellan två versioner
Här visas ändringar i "Methods in Scientific Computing (DD2363), 7.5hp, Spring 2017" mellan 2017-03-06 06:43 av Johan Jansson och 2017-03-07 10:23 av Johan Hoffman.
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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.
Differential equations are used extensively in science and engineering, for example, for virtual design and to model the Laws of Nature.
https://www.youtube.com/watch?v=TSxCFoBgxUw&list=PLsFk6Zk9M10FjIa_jyB5uqE_qydlsQYWc
Links
* FEniCS - open source FEM software
* EUNISON - simulation of the human voice
* FEM simulation of the blood flow in the heart
* FEM simulation of the air past an airplane
* Top 500 list of supercomputers
Course activites
* 16 lectures
* 8 laboratory sessions
Examination
* Written examination, 4.5hp (Grade: A, B, C, D, E, FX, F)
* Written exam based on the lecture notes of the course, and the lab modules Lab1-Lab6.
* Exam maximum 50p: 40p (A), 35p (B), 30p (C), 25p (D), 20p (E), <20p (F)
* Lab modules Lab1-Lab6, 3.0hp (P/F)
* Lab modules: each LabX consists of a set of mandatory problems to complete (P/F) + a set of optional problems that give bonus points for the written exam: max 2p/LabX (max 12p in total).
* Deadline for lab reports: March 147 (After this date no bonus points will be awarded.)
* Lab reports for each module should be submitted online.
Teachers Johan HoffmanOffice hours: Tuesdays 9:00-10:00 (Office 4432, Lindstedtsvägen 5)
Johan JanssonContact person for Lab2-Lab5.
Tania Bakhos Contact person for Lab1 and Lab6.
Niclas Jansson
Van Dang Nguyen
Literature [Lecture notes]
Extra reading [LIN] Trefethen, Bau, "Numerical Linear Algebra", SIAM, (ISBN 978-0-898713-61-9) [SIAM]
[CDE] Eriksson, Estep, Hansbo, Johnson, "Computational Differential Equations", Studentlitteratur, (ISBN 91-44-49311-8), 1996. [Bokus] [Studentlitteratur] [Kårbokhandeln]
NOTE: In some electronic versions of the CDE book, the Chapter 13 "Calculus of Several Variables" may be missing. For the problem sets the correct chapters should be: Chapter 8 "Two-Point Boundary Value Problems", Chapter 15: "The Poisson Equation", Chapter 21: "The Power of Abstraction".
Lab modules Lab1: Iterative methods for solving linear systems [Lab1 - PM][Lab1 - part 1 (Python)][Lab1 - part 2 (Python)][Lab1 - part 1 (Jupyter)][Lab1 - part 2 (Jupyter)][The Conjugate Gradient Method - Shewchuk]
Lab2: ODE time stepping [Lab2 - PM and Jupyter source]
Lab3: FEM assembly [Lab3 - PM and Jupyter source]
Lab4: PDE and FEM in 1D/2D [Lab4 - PM and Jupyter source]
Lab5: Adaptive FEM [Lab5 - PM and Jupyter source]
Lab6: Optimization [Lab6 - PM and Jupyter source]
Software SciPy - Python-based ecosystem of open-source software for mathematics, science, and engineering
FEniCS project - computing platform for partial differential equations (PDE)
Julia linear algebra
Week plan Week 1
* Lecture 1: Vector spaces
* Lecture 2: Matrix algebra
* Lecture 3: Linear systems of equations - direct methods
Week 2
* Lecture 4: Eigenvalues and eigenvectors
* Lecture 5: Iterative methods
* Lab 1: Iterative methods for solving linear systems
Week 3
* Lecture 6: Nonlinear equations - Newton's method
* Lecture 7: ODE - time stepping IVP
* Lab 2: ODE time stepping
Week 4
* Lecture 8: Course review
* Lecture 9: Function approximation - piecewise polynomials, interpolation, LS/L2-projection
* Lecture 10: FEM for 1D BVP model problems
Week 5
* Lecture 11: FEM algorithms - quadrature, mesh, reference element, assembly algorithm
* Lecture 12: PDE - FEM for 2D/3D BVP model problems
* Lecture 13: PDE - semi-discretization of IBVP
Week 6
* Lecture 14: Optimization
* Lecture 15: Adaptive FEM
* Lecture 16: Initial boundary value problems
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