Thu , Oct 1
|
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++,
C++,
C,
LaTeX, python,
numpy, Matlab,
Matlab, MPI,
OpenMP,
CUDA,
- Install Linux in Windows: Use WSL
and install the recent Ubuntu from Microsoft Store (Screenshot).
- 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"
- Linux in Windows: Install WSL
and afterwards ubuntu from the MS-store.
|
Tue, Oct 6
Thu, Oct 8
|
Partial differential equations (PDEs): stationary,
function spaces (notes)
- modelling of heat
conductivity [JL, §2]
- classical formulation; boundary
conditions, function spaces C
- strong formulation, interface
conditions
- special modelling: long/thin domains,
symmetry, rotational symmetry
bash:
make:
|
Tue, Oct 13
Thu, Oct 15
|
Partial differential equations (PDEs): stationary,
function spaces (notes):
- integral formulation (Gauß-Ostrogradski),
differential formulation
- distributions, weak derivative, Sobolev
spaces
(embedding)
[JL, §3.1]
- weak formulation, variational
formulation
- approximation of solution by sum of
basis functions
git: IMSC, Gruppe,
LV.
|
Tue, Oct 20
Thu, Oct 22
|
Discretization of domain (notes):
- elements, vertices
- basis functions with local support:
finite element approximation
- Sobolev 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 27
Thu, Oct 29
|
Some more aspects (notes,
notes):
- existence and uniqueness of solution; Lax-Milgram
Lemma
- compatibility in case of non-uniqueness
- min-max principle (german,
english)
- discrete representation of above continuous theorems
Ex 2
|
Tue, Nov 3
Thu, Nov 5
|
Algorithmic aspects of FEM (notes)
- domain description
- meshing (quality)
- generation of stiffness matrix and right hand side (sparsity
pattern!, reference element): Intro into Finite
Elements: pdf.
Parallelization concept and FEM
- Introduction into hardware and parallel concepts: pdf
(shared memory).
- solving the (linear) system of equations
- Iterative Methods: pdf.
- Geometrisches Multigrid: pdf.
[DHL §7, Vas §5]
- Algebraic Multigrid: pdf.
|
Tue, Nov 10
Thu, Nov 12
|
Parallelization concept and FEM
- Introduction into an FEM code
- Parallel Finite Elements (OpenMP, MPI): pdf.
- Commented code for OpenMP
and for MPI.
- encyclopedia FEM
Ex 3
|
Tue, Nov 17
Thu, Nov 19
|
Tuesday, Nov 18: no lecture
Thursday, Nov. 20: no lecture
|
Tue, Nov 24
Thu, Nov 26
|
Parallelization concept and FEM: GPU
Ex 4
|
Tue, Dec 1
Thu, Dec 3
|
Solving the system of (linear) equations
- Geometrisches Multigrid: pdf.
[DHL §7, Vas §5]
- Algebraic Multigrid: pdf.
- Improved parallelization: pdf,
pdf.
- Non-linear problem: pdf
- Short summary on technical parallelization: pdf
Thursday,
|
Tue, Dec 8
Thu, Dec 10
|
Domain decomposition methods
Ex 5 (shm)
|
Thu, Jan 7
|
Lecture
Ex 7 (MPI)
|
Tue, Jan 12
Thu, Jan 14
|
Lecture
TBA
|
Tue, Jan 19
Thu, Jan 20
|
Consultation
Consultation
|
Tue, Jan 26
Thu, Jan 28
|
Project presentations
|
