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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Linear solvers for the finite pointset method
 Schäfer, M.: Recent Advances in Computational Engineering : Proceedings of the 4th International Conference on Computational Engineering, ICCE 2017, Darmstadt, 2829 September 2017 Cham: Springer International Publishing, 2018 (Lecture notes in computational science and engineering 124) ISBN: 9783319938905 (Print) ISBN: 9783319938912 (Online) ISBN: 3319938908 S.89110 
 International Conference on Computational Engineering (ICCE) <4, 2017, Darmstadt> 

 Englisch 
 Konferenzbeitrag 
 Fraunhofer SCAI () 
Abstract
Many simulations in Computational Engineering suffer from slow convergence rates of their linear solvers. This is also true for the Finite Pointset Method (FPM), which is a Meshfree Method used in Computational Fluid Dynamics. FPM uses Generalized Finite Difference Methods (GFDM) in order to discretize the arising differential operators. Like other Meshfree Methods, it does not involve a fixed mesh; FPM uses a point cloud instead. We look at the properties of linear systems arising from GFDM on point clouds and their implications on different types of linear solvers, specifically focusing on the differences between onelevel solvers and Multigrid Methods, including Algebraic Multigrid (AMG). With the knowledge about the properties of the systems, we develop a new Multigrid Method based on point cloud coarsening. Numerical experiments show that our Multicloud method has the same advantages as other Multigrid Methods; in particular its convergence rate does not deteriorate when refining the point cloud. In future research, we will examine its applicability to a broader range of problems and investigate its advantages in terms of computational performance.