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Coupling Meshbased and Meshfree Methods by a Transfer Operator Approach

Please always quote using this URN: urn:nbn:de:0297-zib-11755
  • In contrast to the well known meshbased methods like the finite element method, meshfree methods do not rely on a mesh. However besides their great applicability, meshfree methods are rather time consuming. Thus, it seems favorable to combine both methods, by using meshfree methods only in a small part of the domain, where a mesh is disadvantageous, and a meshbased method for the rest of the domain. We motivate, that this coupling between the two simulation techniques can be considered as saddle point problem and show the stability of this coupling. Thereby a novel transfer operator is introduced, which interacts in the transition zone, where both methods coexist.

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Metadaten
Author:Konstantin FackeldeyORCiD
Document Type:ZIB-Report
Tag:Gitterlose Methoden; Kopplung; inf-sup-Bedingung
inf-sup-Condition; meshbased; meshfree
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M12 Stability and convergence of numerical methods
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M50 Mesh generation and refinement
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Mxx Basic methods in fluid mechanics [See also 65-XX] / 76M10 Finite element methods
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Mxx Basic methods in fluid mechanics [See also 65-XX] / 76M28 Particle methods and lattice-gas methods
PACS-Classification:00.00.00 GENERAL / 07.00.00 Instruments, apparatus, and components common to several branches of physics and astronomy (see also each subdiscipline for specialized instrumentation and techniques) / 07.05.-t Computers in experimental physics; Computers in education, see 01.50.H- and 01.50.Lc; Computational techniques, see 02.70.-c; Quantum computation architectures and implementations, see 03.67.Lx; Optical computers, see 42.79.Ta / 07.05.Tp Computer modeling and simulation
Date of first Publication:2010/07/02
Series (Serial Number):ZIB-Report (10-12)
ISSN:1438-0064
ZIB-Reportnumber:10-12
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