lecture NMMO403

Something to read...

• Computational Differential Equations, K. Eriksson et al.
• ssh, remote access [web clusteru ↵]
• Introduction to bash shell, bash tutorial ↵
• emacs reference card
• vim reference card
• What every computer scientist should know about floating-point arithmetic (Goldberg, 1991)
• Git book,progit book in czech
• [gitlab service in karlin ↵], [Faculty gitlab service ↵]
• Netlib (Linear algebra software overview by J. Dongarra)

FEniCS

• Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book, A. Logg et al. [full pdf]
• FEniCSx/FEniCS - FEniCS project
• Official FEniCS tutorial, Refference documetnation: 2019.1.0 - python
• → Our own FEniCS tutorial
• Behind FEniCS... Petsc, trilinos
• Next developement... FEniCSx, Firedrake
• On top of FEniCS... CBC, RBniCS, multiphenics, FEniCS shells, phaseflow-fenics, ...
• Other amazing projects: Freefem, Deal.ii, Elmer, openFOAM, MFEM, MoFEM, ...

Syllabus...

Lecture 0 - introduction to python

• basic ideas of Python and how to use it
• using SciPy and NumPy [scipy web ↵]
• [numpy for matlab users ↵]
• basic BLAS operations in python and numpy [numpy-quickstart ↵]
• matrix--vector multiplication

Lecture 1 - introduction to FEniCS

• Lapalce on unit square

Lecture 2 - Heat equation

• timedependent problems

Lecture 3 - convection-diffusion equation

• SUPG and IP stabilizations
• GLS formulation
• image as initial data

Lecture 4 - Navier-Stokes equation

• flow around cylinder benchmark

Lecture 5 - Navier-Stokes equation

• flow around cylinder benchmark, asymptotic tests

Lecture 6 - solvers

• problem and solver clases
• linear algebra backends

Lecture 7 - elasticity

• linear and nonlinear elasticity

Exam tasks pool....

• Anisotropic diffusion benchmark tests [ pdf ]
• NIST set of 2D simple benchmarks with various difficulties [ pdf ]
• DFG benchmark for incompressible Navier-Stokes equations (DFG) [ pdf ]
• The Aerodynamics of Letters
• Heated cavity benchmark (MIT) [ pdf ] or Rayleigh–Bénard convection [ pdf]
• Rising Bubble benchmark [ pdf ]
• Levelset implementation for free surface problems.
  D. Lindbo, Finite Element Computations for a Conservative Level Set Method Applied to Two-Phase Stokes Flow, 2006.
• Lava lamp simulation, another Lava lamp setup
• Various hydrodynamic problems: Flow in Tesla valve, wikipedia, Optimization of Tesla valve
  Fluid control devices, Fluidics, Fluid computers, FLODAC: a pure fluid digital computer
• Flow in Venturi pipe
• Eigenvalues and musical instruments or here
• Image processing: Noise removal by PDE, Image segmentation by level-set method
• Blankenbach benchmark for mantle convection
• Elder problem - flow in porous media
• Pattern formation problems (Grey-Scott model) Complex Patterns in a Simple System, Reaction-Diffusion by the Gray-Scott Model: Pearson's Parametrization
• Epidemic models with spatial diffusion wikipedia: Reaction–diffusion system [ Localized outbreaks in an S-I-R model with diffusion, A fully adaptive numerical approximation for a two-dimensional epidemic model with nonlinear cross-diffusion ]