Webrelaunch 2020

MathSEE lectures

WS 19/20
A first glance at Finite Element implementation
Wed 23.10.2019, Bldg 20:30, SR 0.001, 14:00-17:00
We recall the concept of the Finite Element method and show some
details on the basis of a self-written Matlab code for Poisson-type
problems in 2D. Issues are
-- Data structures (mesh and function representation)
-- Assembly of the system of equations (linear and nonlinear)
-- Boundary conditions (of different types)
-- Boundary approximation
-- Validation (experimental order of convergence)
In a second part we give an introduction into the open source Finite
Element library deal.II (www.dealii.org). Issues are
-- Download and installation
-- How to get help (tutorials, video lectures, support)
-- Realisation of the above enlisted steps
-- How to run a programm (predefined examples)
-- Visualisation with ParaView
-- External libraries (MPI, PetSc, Trilinos)

Prof. Willy Dörfler (IANM), MSc. Fabian Castelli (IANM)
Wissenschaftlicher Nachwuchs

SS 19
PDEs: From Modeling Equations to Scientific Simulation Code
Wed/Thu 24/25.04.2019, Bldg 20:30, SR 1.067, 14:00-17:15

The course covers the central aspects of mathematical modelling using PDEs, and the basics of the finite element method. Furthermore, we will introduce concepts, algorithms, and tools to turn discretized PDEs into scientific computer simulations.
• No deep knowledge in PDEs needed.
• No deep background in Numerics needed.
• No prior programming skills needed.
• No knowledge in Computer Architecture or Computer Science needed.

• Partial Differential Equations
(Modeling, derivation of equations. Potential equation, variational form and weak form, existence of solutions)
• Finite Element Discretization
(Galerkin methods, deriving systems of equations, error bounds. Examples of finite elements, quadrature)
• Finite Difference Discretization
• Linearization of Non-Linear Problems
• Computational Sparse Linear Algebra
• Arithmetic Intensity & Roofline Model
• Direct and Iterative Linear Solvers
• Krylov Subspace Methods
• Preconditioning: block-Jacobi, ILU

• Shell/Terminal Usage
• Access Server
• Deploy RSA keys
• Transfer Files
• Compile and link against Libraries
• Versioning System Usage (Git)
• Continuous Integration (CI) in GitLab
• Unit Testing for Software

Prof. Willy Dörfler (IANM), Dr. Hartwig Anzt (IANM/SCC)
Wissenschaftlicher Nachwuchs