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Methods in Scientific Computing (DD2363), 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. 

Links

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 17 (After this date no bonus points will be awarded.) 
    • Lab reports for each module should be submitted online (emailed to the lab contact person and the course leader).
    • The optional problems for each lab are (each gives max 2p for the written exam):
      • Lab1: Section 2.5-2.6
      • Lab2: Section 2.6.1
      • Lab3: Section 2.3.4
      • Lab4: Section 2.3.2
      • Lab5: Section 2.1.1: Exercise 4 (Try different geometries)
      • Lab6: Section 2 

Teachers

Johan Hoffman
Office hours: Tuesdays 9:00-10:00 (Office 4432, Lindstedtsvägen 5)

Johan Jansson
Contact 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

Lärare Johan Hoffman skapade sidan 3 januari 2017

Johan Hoffman flyttade sidan från Methods in Scientific Computing (DD2363) 3 januari 2017

Lärare Johan Hoffman ändrade rättigheterna 4 januari 2017

Kan därmed läsas av alla inloggade användare och ändras av lärare.

Lärare Johan Hoffman ändrade rättigheterna 5 januari 2017

Kan därmed läsas av alla och ändras av lärare.
Johan Jansson redigerade 3 februari 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.

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 14 (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 distributed in time for the lectures.  

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 Lab4: PDE and FEM in 1D/2D Lab5: Adaptive FEM Lab6: Optimization 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 notes 1]
* Lecture 2: Matrix algebra[Lecture notes 2]
* Lecture 3: Linear systems of equations - direct methods[Lecture notes 3]
Week 2 
* Lecture 4: Eigenvalues and eigenvectors[Lecture notes 4]
* Lecture 5: Iterative methods[Lecture notes 5]
* Lab 1: Iterative methods for solving linear systems
Week 3 
* Lecture 6: Nonlinear equations - Newton's method[Lecture notes 6]
* Lecture 7: ODE - time stepping IVP[Lecture notes 7] 
* 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 - Adaptive FEM
* Lecture 15: Optimization - Parameter estimation
* 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

kommenterade 25 februari 2017

I have a question about the first lab that might concern everyone: what kind of answer do you exactly expect for the GMRES exercice? Looks unclear to me.

Thanks!

Anmäl missbruk
kommenterade 26 februari 2017

Another thing: since yesterday I cannot access http://ec2-35-166-131-79.us-west-2.compute.amazonaws.com/, am I the only one in this case?

Anmäl missbruk
Johan Jansson redigerade 27 februari 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 14 (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 distributed in time for the lectures.  

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 Lab5: Adaptive FEM Lab6: Optimization 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 notes 1]
* Lecture 2: Matrix algebra[Lecture notes 2]
* Lecture 3: Linear systems of equations - direct methods[Lecture notes 3]
Week 2 
* Lecture 4: Eigenvalues and eigenvectors[Lecture notes 4]
* Lecture 5: Iterative methods[Lecture notes 5]
* Lab 1: Iterative methods for solving linear systems
Week 3 
* Lecture 6: Nonlinear equations - Newton's method[Lecture notes 6]
* Lecture 7: ODE - time stepping IVP[Lecture notes 7]
* Lab 2: ODE time stepping
Week 4 
* Lecture 8: Course review 
* Lecture 9: Function approximation - piecewise polynomials, interpolation, LS/L2-projection[Lecture notes 8]
* 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 notes 14]
* 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

Johan Jansson redigerade 27 februari 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 14 (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 distributed in time for the lectures.  

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 Lab5: Adaptive FEM Lab6: Optimization 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 notes 1]
* Lecture 2: Matrix algebra[Lecture notes 2]
* Lecture 3: Linear systems of equations - direct methods[Lecture notes 3]
Week 2 
* Lecture 4: Eigenvalues and eigenvectors[Lecture notes 4]
* Lecture 5: Iterative methods[Lecture notes 5]
* Lab 1: Iterative methods for solving linear systems
Week 3 
* Lecture 6: Nonlinear equations - Newton's method[Lecture notes 6]
* Lecture 7: ODE - time stepping IVP[Lecture notes 7]
* Lab 2: ODE time stepping
Week 4 
* Lecture 8: Course review 
* Lecture 9: Function approximation - piecewise polynomials, interpolation, LS/L2-projection[Lecture notes 9]
* Lecture 10: FEM for 1D BVP model problems[Lecture notes 10]  
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 notes 14]
* 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

Johan Jansson redigerade 27 februari 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 14 (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 distributed in time for the lectures.  

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 Lab5: Adaptive FEM Lab6: Optimization 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 notes 1]
* Lecture 2: Matrix algebra[Lecture notes 2]
* Lecture 3: Linear systems of equations - direct methods[Lecture notes 3]
Week 2 
* Lecture 4: Eigenvalues and eigenvectors[Lecture notes 4]
* Lecture 5: Iterative methods[Lecture notes 5]
* Lab 1: Iterative methods for solving linear systems
Week 3 
* Lecture 6: Nonlinear equations - Newton's method[Lecture notes 6]
* Lecture 7: ODE - time stepping IVP[Lecture notes 7]
* Lab 2: ODE time stepping
Week 4 
* Lecture 8: Course review 
* Lecture 9: Function approximation - piecewise polynomials, interpolation, LS/L2-projection[Lecture notes 9]
* Lecture 10: FEM for 1D BVP model problems[Lecture notes 10]  
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 notes 14]
* 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

Johan Jansson redigerade 28 februari 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 14 (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 Lab6: Optimization 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

Johan Jansson redigerade 28 februari 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 14 (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 Lab6: Optimization 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

Johan Jansson redigerade 2 mars 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 14 (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 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

Johan Jansson redigerade 6 mars 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 14 (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

kommenterade 7 mars 2017

According to the course web there will be bonus questions in the lab, but there aren't any optional questions in the lab materials except for the one used in lab 1. Which ones re the bonus questions for lab 2-6? Also is the deadline of the labs before 14th March or before the exam(17th)?

Anmäl missbruk
Lärare kommenterade 7 mars 2017

The deadline is before the exam the 17th, the date for the exam was originally March 15. This is now updated. Regarding bonus questions I will get back to this later today.

/Johan

Anmäl missbruk
Lärare kommenterade 7 mars 2017

This is now updated on the course website, under "Examination". 

/Johan

Anmäl missbruk
kommenterade 7 mars 2017

It's been one week that I cannot access http://ec2-35-166-131-79.us-west-2.compute.amazonaws.com/. My first two labs are hosted on this plateform and I would like to access it in order to finish my reports. Can anyone help?

Anmäl missbruk
Lärare kommenterade 7 mars 2017

Hi Aurélien,

You should have been sent credentials for the new machine:

http://ec2-52-39-233-4.us-west-2.compute.amazonaws.com

which you can use for the course, can you login to that?

The files on the machines are not stored on disk, so you should always download all the files to your own computer regularly. If you believe you have lost some files, please contact me directly by mail at jjan@kth.se .

Best,

  Johan

Anmäl missbruk
kommenterade 7 mars 2017

Hi,

Yes, this one works for me. I did not understand that we were going to loose the files on the first machine, my bad. I did indeed loose the files from Lab 1 and Lab 2 -- but that's fine, I will make up for it.

Thank you!

Anmäl missbruk
En användare har tagit bort sin kommentar
kommenterade 7 mars 2017

The instance was unreachable for a while before I was online again. I am unable to login now.

Anmäl missbruk
Lärare kommenterade 7 mars 2017

Hi Wei,

The instance has been rebooted, the new passwords should hopefully be sent out shortly, in the worst case tomorrow.

Best,

  Johan

Anmäl missbruk
kommenterade 7 mars 2017

Hi,

I was trying uniform refinement in lab 5 by setting adaptive = False before it was unreachable, did I crash it?

Anmäl missbruk
En användare har tagit bort sin kommentar
En användare har tagit bort sin kommentar
kommenterade 10 mars 2017

Hi,

At the end of Assignment 4, it is ask to make \(c_0\) and \(c_1\) react to produce \(c_2\). I've tried different things but I don't manage to make it work.

In fact, I don't really understand why \(\gamma((c_0c_1,z_0)+(c_0c_1,z_1))\) represents the elimination of \(c_0\)and \(c_1\) when they meet.

Anyone mind giving a hint?

Anmäl missbruk
Lärare kommenterade 13 mars 2017

Hi Aurelien,

Here's a similar lab sheet which could give more help:

http://www.bodysoulmath.org/sessions/f5/instructions/pdf/session-e5.pdf

Multiplying by z[0] means that term belongs to the equation for c[0]. The other term in that equation is the time derivative coming from (inner(c - c0, z)/k. So for c_0 you have the equation:

\dot{c_0} = -gamma c_0 c_1

Since gamma, c_0 and c_1 are always positive, this can be interpreted as exponential decay of c_0 with gamma and c_1 acting as coefficients. You then have the corresponding equation for c_1. Is it clearer now?

Anmäl missbruk
kommenterade 14 mars 2017

Yes, definitely clearer! Thank you very much.

Anmäl missbruk
kommenterade 15 mars 2017

The instance is unresponsive. Also, I find that when I increase the adapt ratio to a certain percentage as instructed by lab 5 Q2, the site will crash.

Anmäl missbruk