Numerical methods for continuum mechanics
Numerische Methoden der Kontinuumsmechanik

Thomas Wick
Katrin Mang

SS 2020
Institut fuer Angewandte Mathematik
Leibniz Universitaet Hannover
==========================================


Website
-------
http://www.thomaswick.org/lehre.html


Zeiten und Ort (Apr 14 - Jul 23, 2020)
--------------------------------------

Di (VL):  12.00 - 14.00 C311
Do (VL):  10.00 - 12.00 C311
Mo (Ueb): 14.00 - 16.00 C311


Sprache / Language
------------------

voraussichtlich English;
bei explizitem Wunsch auch gerne in Deutsch


Literatur
---------
[1] T. Wick; Modeling, Discretization, Optimization, and Simulation of Fluid-Structure Interaction;
    lecture notes, Feb 2020

    --> Skriptum wird während des Semesters leicht angepasst werden (Typos, ...).

    Slightly older online version:
    http://www.thomaswick.org/links/lecture_notes_FSI_Nov_28_2019.pdf


[2] R. Rannacher; Numerik 3: Probleme der Kontinuumsmechanik und ihre 
    numerische Behandlung
    https://heiup.uni-heidelberg.de/catalog/book/312

[3] T. Richter; Fluid-Structure Interactions, Springer 2017
    https://www.springer.com/de/book/9783319639697

[4] T. Wick; Numerical methods for partial differential equations;
    Hannover : Institutionelles Repositorium der Leibniz Universitaet Hannover,
    Jan 2020: DOI
    https://doi.org/10.15488/9248



Uebungsaufgaben
---------------

weakly excercises



Detailliere Planung
===================


April
-----

V1 (Apr 14, 2020): 
   [4] Chapter 13: 
    i) Nonlinear equations: examples
    ii) Solution methods (fixed-point) nonlinear equations
       

V2 (Apr 16, 2020)
   [4] Chapter 13:
    i)  Directional derivatives
    ii) Newton's method in Banach spaces


V3 (Apr 21, 2020)
   [4] Section 13.15
    i) Temporal discretization of nonlinear, time-dependent PDEs
    ii) Section 13.16

V4 (Apr 22, 2020)
   [4] Chapter 14:
    i) Introduction to coupled problems: examples
    ii) Classifications: interface-coupled - volume coupled
    iii) Section 14.1 (Interface 1D)

V5 (Apr 28, 2020)
   [4] Chapter 14: 
    i) Section 14.6 (Variational-monolithic coupling)
    ii) Interface coupling

V6 (Apr 30, 2020)
   [4] ggf. continuing Chapter 14 if necessary


May 
---

V7 (May 5, 2020)
  [1] Section 2.7: Continuum mechanics: challenges FSI
  [1] Chapter 5: Kinematics

V8 (May 7, 2020)
  [1] Section 5.2: Balance principles
      also discuss incompressibilities in fluids and solids

V9 (May 12)
  [1] Section 5.3: constitutive laws and Navier-Stokes equations

V10 (May 14)
  [1] Section 5.4: modeling solids mechanics

V11 (May 19)
  [1] Section 5.4 (Continuing if necessary)
      Section 5.5: Summarizing the equations


CHRISTI HIMMELFAHRT (May 21, 2020)

V12 (May 26)
  [1] Chapter 6, 
      i) Section 6.2: Weak formulations NSE
     ii) Outflow boundary conditions
    iii) Symmetric vs. non-symmetric Cauchy stress
      

V13 (May 28)
  [1] Section 6.3 : well-posedness Stokes (stationary NSE?!)
      Lit. Roger Temam for the latter


June
----

PFINGSTEN

V14 (Jun 9):
   [1] Chapter 6.4: Weak formulations of elasticity
       Well-posedness of linearized stationary elasticity

V15 (Jun 11):
   [1] Chapter 7: Modeling fluid-structure interaction;
      Techniques

V16 (Jun 16)
   [1] Chapter 7.3: ALE-FSI; explanation of ALE mappings (interface-tracking)
       Chapter 7.3: Interface coupling conditions, mesh motion, etc.

V17 (Jun 18)
   [1] Chapter  7.3.8: FSI in a variational-monolithic setting


V18 (Jun 23)
   [1] Chapter 7.3.14: Existence of stat. ALE-FSI (Grandmont 2002; Wick/Wollner; 2019)


V19 (Jun 25)
   [1] Chapter 8: Temporal discretization
       i) One-Step-theta
      ii) Fractional-Step-theta

V20 (Jun 30)
   [1] Chapter 8: Spatial discretization (FEM)
      i) inf-sup condition in Stokes / Navier-Stokes
     ii) inf-sup condition in nearly incompressible materials
     iii) FEM-discretization of ALE-FSI


July 
----

V21 (Jul 2)
   Coping with the discrete inf-sup conditions (Taylor Hood, special elements, ...)

V22 (Jul 7)
   [1] Chapter 9: Formally Newton (now easy since done in V2 in detail)
       Arising linear equation systems

V23 (Jul 9)
   [1] Chapter 9: Analyzing the structure of the linear equation
       systems, constructing preconditioners, ...

V24 (Jul 14)
   Further topics in continuum mechanics: non-isothermal processes;
   e.g., thermo-poroelasticity: coupling solics, flow, temperature

V25 (Jul 16)
   Continuing V24

V26 (Jul 21)
   Further topics in continuum mechanics

V27 (Jul 23)
   Summary and outlook