Thu , Oct 2

Hardware resources (login from outside KFU only via  VPN):

• Mephisto at IMSC, or via jupyter-Server des IMWR.
• Remote login to servers:
• VPN to KFU is needed: install via VPN Service the software AnyConnect (configure as server: https://univpn.uni-graz.at;   login: KFU E-mail)
• Linux: use ssh -X  143.50.47.xxx to connect to compute server
• Windows: Install WinnSSHTerm with a guided installation of further packages (putty, winscp, X-Server)

Recall your C++:

• CheatSheet: C++, LaTeX, python, numpy, Matlab, MPI, OpenMP, CUDA,
• Passing parameters to/from functions; Classes (member, methods, encapsulation, inheritance)
  
• Memory costs of containers (1, 2, 3); deep copy vs. shallow copy (notes); nullptr, const_expression, static_assert;
• smart pointer [Examples: variants_pointer, shared, unique];
• exception handling (predefined exceptions, tutorial) [Examples: file_io, myvector];
• Multi Threading in C++-17 (Bartek's coding blog, sort) [Example: thread_17];
  Linker requires option  -ltbb
• Type-checking at compile time: C++17: type_traits, C++20 concepts, 
• Ranges in C++20.
• Further literature: "The C++ Standard Library"; "C++20: Get the Details"

Tue, Oct 7
Thu, Oct 9

Partial differential equations (PDEs): stationary, function spaces

• modelling of heat conductivity
• classical formulation; boundary conditions, function spaces C
  
• strong formulation, interface conditions

---

bash:

• Bash cheatsheet [Rehan, quickme]
• Intro into Linux (Wie werde ich UNIX-Guru? (OpenBook)):
• command line arguments, redirection, pipelining, tools (example; myvector_ext, BinaryMatrix).
• bash scripts (ex)

make:

• simple tutorial, cheatsheet (§ 1.4 in pdf),
• Preprocessor (Howto)
• Example: Mixing of C/C++/Fortran (code)

Tue, Oct 14
Thu, Oct 16

Partial differential equations (PDEs): stationary, function spaces:

• distributions, weak derivative, Sobolev spaces (embedding)
• weak formulation, variational formulation
• approximation of solution by sum of basis functions

---

git: git-Gruppe

• git cheatsheets (1,2)
• README.md and its basic syntax.
• (basics, simple intro, learn git in 15 min)

Tue, Oct 21
Thu, Oct 23

Discretization of domain:

• elements, vertices
• basis functions with local support: finite element approximation
  
• Sobolov spaces
  
• variational formulation, Galjorkin method
  Schellbach (1851, 2024)
  
• discrete representation of the continuous PDE problem
• sparse system of equations: stiffness matrix, load vector
  
• higher order basis functions

---

Ex 1

Tue, Oct 28
Thu, Oct 30

Some more aspects

• existence and uniqueness of solution; Lax-Milgram Lemma
• compatibility in case of non-uniqueness
• min-max principle
• discrete representation of above continuous theorems

---

Ex 2

Tue, Nov 4
Thu, Nov 6

Algorithmic aspects of FEM

• domain description
• meshing
• generation of stiffness matrix and right hand side (sparsity pattern!, reference element): Intro into Finite Elements:  pdf.
• solving the (linear) system of equations
• Iterative Methods: pdf. 
• Geometrisches Multigrid:  pdf. [DHL §7, Vas §5]
• Algebraic Multigrid: pdf.
• Introduction into an FEM code

---

Parallelization concept and FEM

• Introduction into hardware and parallel concepts:  pdf.

Tue, Nov 11
Thu, Nov 13

Parallelization concept and FEM

• Parallel Finite Elements (OpenMP, MPI):  pdf.
•  Commented code for OpenMP and for MPI.

---

Ex 3

Tue, Nov 18
Thu, Nov 20

Parallelization concept and FEM

• GPU

---

TBA

Tue, Nov 25
Thu, Nov 27

Domain decomposition methods

• Schur complement, Schur complement method (Element-by-Element method) [DHL §2.3, Vas §3.1.1]
• Multiplicative Schwarz method  [Vas §7.7]
• Additive Schwarz method [Vas §7.8]

---

Ex 4

Tue, Dec 2
Thu, Dec 4

Vorlesung

---

TBA

Tue, Dec 9
Thu, Dec 11

Vorlesung

---

Ex 5

Thu, Jan 8

Vorlesung

---

Ex 6

Tue, Jan 13
Thu, Jan 15

Vorlesung

---

TBA

Tue, Jan 20
Thu, Jan 22

Consultation

---

Consultation

Tue, Jan 27
Thu, Jan 29

Project presentations