Syllabus
● The Arbitrary Lagrangian-Eulerian method and free boundary problems
● Nitsche's method - weak formulation of boundary conditions, application to boundary conditions at geometrically non-trivial interfaces and to the kinematic equation of the free surface
● The Cahn-Hilliard-Navier-Stokes equations
● The Nédélec finite element and Maxwell's equations
● The Stefan problem and the enthalpy method
● Augmented Lagrangian method and problems with inequality constraints, contact problems
● Spherical harmonic functions and solving problems on the sphere/ball
● Pressure-robust methods for incompressible flow
● Adaptivity for spatial discretization
Annotation
The course is a follow-up of NMMO403 Computer Solution of Continuum Physics Problems and is focused on the numerical implementation of more advanced computational techniques from various parts of physics. Focus on the use of HPC, academic open source software.