Difference between revisions of "CompactCourse: Introduction to parallel-in-time and other new time-stepping methods - Summer19"

From Sccswiki
Jump to navigation Jump to search
Line 4: Line 4:
 
| timeplace = block course August 26-30, 2019, time: 9:00 - 10:30 and 13:00 - 14:30, room 02.07.023
 
| timeplace = block course August 26-30, 2019, time: 9:00 - 10:30 and 13:00 - 14:30, room 02.07.023
 
| credits = 1 credit
 
| credits = 1 credit
| audience = all interested students, in particular students of BGCE, TopMath, CSE, Mathematics, and Informatics
+
| audience =  
 +
All students interested in simulation of time depending problems, in
 +
particular students of BGCE, TopMath, CSE, Mathematics, Informatics and
 +
Mechanical/Electrical Engineers
 
| tutorials = -
 
| tutorials = -
 
| exam = programming assignment and written short report
 
| exam = programming assignment and written short report
Line 12: Line 15:
 
= News =
 
= News =
 
* July 29: The compact course is now open for registration. Please contact [mailto:d.ruprecht@leeds.ac.uk Daniel Ruprecht], [mailto:martin.schreiber@tum.de Martin Schreiber], and [mailto:neckel@in.tum.de Tobias Neckel] in one mail directly.
 
* July 29: The compact course is now open for registration. Please contact [mailto:d.ruprecht@leeds.ac.uk Daniel Ruprecht], [mailto:martin.schreiber@tum.de Martin Schreiber], and [mailto:neckel@in.tum.de Tobias Neckel] in one mail directly.
 +
 +
= Prerequisites =
 +
Although there will be a brief introduction to ordinary and partial
 +
differential equations and time integration methods, students are
 +
expected to be already familiar with them. A working knowledge of
 +
standard numerical methods such as finite differences, Runge-Kutta
 +
methods, etc. would be very helpful, but is not necessary. To fully
 +
benefit from the course, students will be given a range of programming
 +
assignments. Experience with Python will therefore be greatly
 +
beneficial.
  
 
= Format of the Course =
 
= Format of the Course =
The course will be a compact course consisting of 4 consecutive half days of lecture and discussions. Groups consisting of 3-4 students will implement programming assignments in Python. Each participant has to hand in a short report of 1 page on brief exercise tasks until Friday, Aug. 30, 11:00.
+
This is a compact course on time integration methods. A brief
 +
introduction to existing time integration methods as well as space
 +
discretization and PDE solvers will be given. Based on this, novel time
 +
integration methods such as parallel-in-time methods, exponential
 +
integration and variants of this will be discussed.
 +
 
 +
The course consists of 4 consecutive half days of lectures,
 +
discussions and assignments. Groups consisting of 3-4 students will
 +
implement programming assignments in Python.  
 +
 
 +
Project report:
 +
Each '''individual''' participant has to hand in a short report of 1 to 2
 +
pages on brief exercise tasks until Sunday, Sept. 1st, 12:00.
  
 
= Content =
 
= Content =
Line 24: Line 49:
 
* Exponential Integration
 
* Exponential Integration
 
* Semi-Lagrangian methods
 
* Semi-Lagrangian methods
 +
 +
 +
= Schedule & Content (preliminary) =
 +
* Time integration basics (Day 1, Session 1)
 +
** HPC challenges
 +
** ODEs and PDEs
 +
*** linear/non-linear ODEs + examples
 +
*** linear/non-linear PDEs + examples
 +
- Runge-Kutta time integrators
 +
  + Explicit RK
 +
  + Butcher table
 +
  + Implicit RK
 +
  + Pade approximations
 +
- Convergence, Consistency and Stability
 +
- Stability function
 +
- CFL condition
 +
- Splitting methods
 +
 +
* Parareal (ODE) (Day 1, Session 2)
 +
 +
* Space discretization and PDE solvers (Day 2, Session 1)
 +
- Space discretization (1D)
 +
  + Global basis functions
 +
    - Trigonometric (Fourier)
 +
    - High-order polynomials (Chebychev)
 +
  + Local basis functions
 +
    - Overlapping
 +
      + Nodal with local interpolation (FD)
 +
      + Superposition of local basis functions (FEM)
 +
    - Non-overlapping
 +
      + Continuous (SEM)
 +
      + Discontinuous (DG)
 +
 +
- Space discretization (nD)
 +
    + Spherical harmonics
 +
 +
- Time integration of PDEs
 +
  + Global spectral
 +
    - Fourier
 +
    - Spherical Harmonics
 +
  + Finite differences
 +
  + Finite elements
 +
    - Classical finite elements
 +
    - Galerkin methods
 +
      + Spectral elements (continuous Galerkin methods)
 +
      + Discontinuous Galerkin methods
 +
 +
  + (Dispersion errors)
 +
    - Theory
 +
    - Normal mode analysis
 +
 +
* Parareal (PDE) (Day 2, Session 2)
 +
 +
* Exponential integrator methods (Day 3, Session 1)
 +
  - Rational approximation of exponential integrators (REXI)
 +
    + Terry-REXI
 +
    +  Cauchy-REXI
 +
    +  Butcher-REXI
 +
  - ETDnRK methods
 +
  - Integrating factor method for direct solution
 +
  - Strang splitting
 +
  - REXI with spherical harmonics
 +
 +
* Spectral Deferred Correction (SDC) Methods (Day 3, Session 2)
 +
 +
* Multi-level SDC + PFASST (Day 4, Session 1)
 +
 +
* Lagrangian methods (Day 4, Session 2)
  
 
== Material ==
 
== Material ==

Revision as of 11:56, 13 August 2019

Term
Summer 19
Lecturer
Dr. Daniel Ruprecht, University of Leeds, Dr. Martin Schreiber, TUM; contact: Dr. rer. nat. Tobias Neckel
Time and Place
block course August 26-30, 2019, time: 9:00 - 10:30 and 13:00 - 14:30, room 02.07.023
Audience
All students interested in simulation of time depending problems, in

particular students of BGCE, TopMath, CSE, Mathematics, Informatics and Mechanical/Electrical Engineers

Tutorials
-
Exam
programming assignment and written short report
Semesterwochenstunden / ECTS Credits
1 credit
TUMonline
n.a.



News

Prerequisites

Although there will be a brief introduction to ordinary and partial differential equations and time integration methods, students are expected to be already familiar with them. A working knowledge of standard numerical methods such as finite differences, Runge-Kutta methods, etc. would be very helpful, but is not necessary. To fully benefit from the course, students will be given a range of programming assignments. Experience with Python will therefore be greatly beneficial.

Format of the Course

This is a compact course on time integration methods. A brief introduction to existing time integration methods as well as space discretization and PDE solvers will be given. Based on this, novel time integration methods such as parallel-in-time methods, exponential integration and variants of this will be discussed.

The course consists of 4 consecutive half days of lectures, discussions and assignments. Groups consisting of 3-4 students will implement programming assignments in Python.

Project report: Each individual participant has to hand in a short report of 1 to 2 pages on brief exercise tasks until Sunday, Sept. 1st, 12:00.

Content

  • Introduction to ODEs/PDEs and standard time integration methods

(Runge-Kutta, explicit/implicit, linear/non-linear, splitting methods)

  • Parareal
  • ML-SDC
  • PFASST
  • Exponential Integration
  • Semi-Lagrangian methods


Schedule & Content (preliminary)

  • Time integration basics (Day 1, Session 1)
    • HPC challenges
    • ODEs and PDEs
      • linear/non-linear ODEs + examples
      • linear/non-linear PDEs + examples
- Runge-Kutta time integrators
  + Explicit RK
  + Butcher table
  + Implicit RK
  + Pade approximations
- Convergence, Consistency and Stability
- Stability function
- CFL condition
- Splitting methods
  • Parareal (ODE) (Day 1, Session 2)
  • Space discretization and PDE solvers (Day 2, Session 1)
- Space discretization (1D)
  + Global basis functions
    - Trigonometric (Fourier)
    - High-order polynomials (Chebychev)
  + Local basis functions
    - Overlapping
      + Nodal with local interpolation (FD)
      + Superposition of local basis functions (FEM)
    - Non-overlapping
      + Continuous (SEM)
      + Discontinuous (DG)
- Space discretization (nD)
   + Spherical harmonics
- Time integration of PDEs
  + Global spectral
    - Fourier
    - Spherical Harmonics
  + Finite differences
  + Finite elements
    - Classical finite elements
    - Galerkin methods
      + Spectral elements (continuous Galerkin methods)
      + Discontinuous Galerkin methods
  + (Dispersion errors)
    - Theory
    - Normal mode analysis
  • Parareal (PDE) (Day 2, Session 2)
  • Exponential integrator methods (Day 3, Session 1)
 - Rational approximation of exponential integrators (REXI)
   + Terry-REXI
   +  Cauchy-REXI
   +  Butcher-REXI
 - ETDnRK methods
 - Integrating factor method for direct solution
 - Strang splitting
 - REXI with spherical harmonics
  • Spectral Deferred Correction (SDC) Methods (Day 3, Session 2)
  • Multi-level SDC + PFASST (Day 4, Session 1)
  • Lagrangian methods (Day 4, Session 2)

Material

t.b.a.