The aim of this project is the development and construction of
Algebraic MultiGrid (AMG) methods. AMG methods try to mimic
geometric multigrid methods just by knowing single grid information
but retaining the optimality of the method. Since the construction
of an universal AMG method for all arising situations in practice
is an unrealistic dream, we will assemble efficient and robust
solvers for special classes of matrices such as large scale systems
arising from the (FEM, FDM, FIT, BEM) discretization of:
Anisotropic Potential Equation
Stokes / Navier-Stokes Equations
Navier-Stokes-flow past a half-opened valve.
(Geometry provided by AVL List GmbH)
quarter of a magnetic valve
Moreover, parallelization of AMG method is an important task,
because it is the main source for a further enhancement of
efficiency in real life applications.
The diploma theses topic can be combined with the
"Project Seminar" held every
spring term at the
Institute ofComputational Mathematics.
Additionally the diploma theses consists in a special application
from industry. The proposed topics should be seen as a collection
of possible subjects. Other suggestions are warmely welcome.
Algebraic Multigrid Methods for Navier-Stokes Equations
Algebraic Multigrid Methods for Convection Diffusion
Algebraic Multigrid Methods on Parallel Computers
Algebraic Multigrid Methods in Structural Mechanics
Algebraic Multigrid Methods for Maxwell's Equations
Algebraic Multigrid Methods for Helmholtz Equations