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

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| term = Summer 19
 
| term = Summer 19
 
| lecturer = [https://engineering.leeds.ac.uk/staff/741/dr_daniel_ruprecht Dr. Daniel Ruprecht, University of Leeds], [https://www.caps.in.tum.de/en/staff/martin-schreiber/ Dr. Martin Schreiber, TUM]; contact: [[Dr. rer. nat. Tobias Neckel]]
 
| lecturer = [https://engineering.leeds.ac.uk/staff/741/dr_daniel_ruprecht Dr. Daniel Ruprecht, University of Leeds], [https://www.caps.in.tum.de/en/staff/martin-schreiber/ Dr. Martin Schreiber, TUM]; contact: [[Dr. rer. nat. Tobias Neckel]]
| timeplace = block course August 26-29, 2019, time: 9:00 - 12:00??, room t.b.a.
+
| timeplace = block course August 26-30, 2019, time: 9:00 - 10:30 and 12:00 - 13:30, 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 11: Line 14:
  
 
= News =
 
= News =
* date t.b.d.: 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 =
t.b.a.
+
* 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)
 +
 
 +
* Project work (Day 5, Sessions 1 + 2)
  
== Material ==
 
t.b.a.
 
  
  
 
[[Category:Teaching]]
 
[[Category:Teaching]]

Latest revision as of 10:37, 27 November 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 12:00 - 13:30, 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)
  • Project work (Day 5, Sessions 1 + 2)