Iterative solvers for PDEs (SS 23)

Basic information

• Lecture: Dietmar Gallistl
• Exercise classes: Dr. Christos Pervolianakis
• Dates:see Lecture in Friedolin and Exercise classes in Friedolin

Further information

• The exam can be taken over 3, 6, or 9 ECTS points. We offer four variants:
  INFORMATION ON THE ORAL EXAMS
  • 3 ECTS exam on Chapters 1+2 (except §1.4), no exercises
  • 6 ECTS exam Variant A: on Chapter 1 (except §1.4), Chapter 2, and §3.1-§3.4, Exercises A1-39 and B1-10
  • 6 ECTS exam Variant B: full lecture (except §1.4), no exercises
  • 9 ECTS exam on the full lecture with exercises
• Required prerequisites: Basic lectures in Analysis, Linear Algebra, Numerical Analysis
• There are no objections for BSc Students to attend the lecture.
• Examination: oral exams on individual appointment

Literature

• Lecture notes on computational PDE, U Jena, 2021.
• Lecture notes on difference schemes, U Jena, 2022.
• D. Braess. Finite elements. Theory, fast solvers and applications in solid mechanics. 3rd ed. Cambridge: Cambridge University Press, 2007.
• S. C. Brenner, L. R. Scott. The mathematical theory of finite element methods. 3rd ed. Texts in Applied Mathematics 15. New York, 2008.

Lecture notes and software

• Lecture notes as pdf file (last update 07-July-2023)
• The exercises are included in the same file as the lecture notes.
• An introduction to Python in German or English as Jupyter notebook.
• Software:
  • A possible implementation of the FDM on the square domain: FDM_square.py
  • Some example on the L-shaped domain: FDM_L.py
  • Implementation of PCG with SSOR preconditioning for the FDM system: pcg_ssor_study.py
  • A basic implementation of FDM multigrid: mg_teach.py
  • Finite element mesh refinement: red_refine.py
  • Basic plotting for the FEM: plot_test.py
  • An example implementation of the FEM: fem_example.py
  • Very basic implementation of the FEM W-cycle: fem_mg.py

• Problem solving: Exercises are issued each Tuesday. The table below displays the exercises to be discussed in the respective week (e.g., the exercises formulated in week 15 can be found in the row for week 16).
• Legend:

  yellow=lecture

  cyan=tutorial

  magenta=self-study

  red=public holiday

  
  

• Week	Monday	Tuesday	Friday	Exercises	Syllabus
  14	3 Apr	4 Apr	7 Apr	A1,2,8,9,10,11,B1	§1.1,§1.2
  15	10 Apr	11 Apr	14 Apr		§1.2,§1.3,§2.1
  16	17 Apr	18 Apr	21 Apr	A3,4,5,B2,3,4	§2.1,§2.2,§2.3
  17	24 Apr	25 Apr	28 Apr	A12,13,14,15,B5	§2.3,§2.4,§2.5
  18	1 May	2 May	5 May		§2.5,§2.6,§2.7,§2.8
  19	8 May	9 May	12 May	A16,17,18,19,20,21,22,23, B8,9	§2.8,§2.9
  20	15 May	16 May	19 May	A24,25,26,27,28	§2.9,§2.10,§2.11 Fig. 2.3-2.4, Def.2.55, Problem_A.30
  21	22 May	23 May	26 May	A29,30,31,B10	§3.1,§3.2
  22	29 May	30 May	2 Jun		§3.2,§3.3,§3.4
  23	5 Jun	6 Jun	9 Jun	A32,33,34,35,36,37,38,39	§3.5,§3.6
  24	12 Jun	13 Jun	16 Jun	A40,41,42,43,B11	§3.7,§4.1
  25	19 Jun	20 Jun	23 Jun	A44,45,46,B12	§4.2
  26	26 Jun	27 Jun	30 Jun	A47,48,49,50,B13	§4.2,§4.3,§4.4
  27	3 Jul	4 Jul	7 Jul	Q&A	§4.4,§4.5