Article (Scientific journals)
Space-Time Meshfree Collocation Method for PDEs
Netuzhylov, Hennadiy; Zilian, Andreas
2009In Proceedings in Applied Mathematics and Mechanics, 9 (1), p. 651--652
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Abstract :
[en] An innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of nonlinear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh-based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods which do not have any underlying mesh, but work on a set of nodes only, without an a priori node-to-node connectivity. A regularization technique to overcome the singularity-by-construction and to compute all necessary derivatives of the kernel functions is presented. The method combines the simplicity and straightforwardness of the strong-form computational techniques with the advantages of meshfree methods over the classical ones, especially for coupled engineering problems involving moving interfaces. The key features of the proposed approach are: (i) no need to generate a mesh, (ii) simplified imposition of boundary conditions, (iii) no need to evaluate integral forms of governing equations, (iv) applicability to complex irregularly-shaped domains. The proposed STMCM is applied to linear and nonlinear ordinary and partial differential equations of different types and its accuracy and convergence properties are studied. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Disciplines :
Mathematics
Author, co-author :
Netuzhylov, Hennadiy
Zilian, Andreas  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit
Language :
English
Title :
Space-Time Meshfree Collocation Method for PDEs
Publication date :
2009
Journal title :
Proceedings in Applied Mathematics and Mechanics
ISSN :
1617-7061
Publisher :
WILEY-VCH Verlag
Volume :
9
Issue :
1
Pages :
651--652
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
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since 18 November 2013

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