Nick, Fabian Pascal: Algebraic Multigrid for Meshfree Methods. - Bonn, 2020. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
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author = {{Fabian Pascal Nick}},
title = {Algebraic Multigrid for Meshfree Methods},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2020,
month = feb,

note = {This thesis deals with the development of a new Algebraic Multigrid method (AMG) for the solution of linear systems arising from Generalized Finite Difference Methods (GFDM). In particular, we consider the Finite Pointset Method, which is based on GFDM. Being a meshfree method, FPM does not rely on a mesh and can therefore deal with moving geometries and free surfaces is a natural way and it does not require the generation of a mesh before the actual simulation.
In industrial use cases the size of the linear systems often becomes large, which means that classical linear solvers often become the bottleneck in terms of simulation run time, because their convergence rate depends on the discretization size.
Multigrid methods have proven to be very efficient linear solvers in the domain of mesh-based methods. Their convergence is independent of the discretization size, yielding a run time that only scales linearly with the problem size. AMG methods are a natural candidate for the solution of the linear systems arising in the FPM, as this thesis will show. They need to be tuned to the specific characteristics of GFDM, though. The AMG methods that are developed in this thesis achieve a speed-up of up to 33x compared to the classical linear solvers and therefore allow much more accurate simulations in the future.},

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