Reference : Space-time meshfree collocation method: Methodology and application to initial-bounda...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
Space-time meshfree collocation method: Methodology and application to initial-boundary value problems
Netuzhylov, H. [Computational Sciences in Engineering, Technische Universität Braunschweig, Beethovenstr. 51, 38106 Braunschweig, Germany]
Zilian, Andreas mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
International Journal for Numerical Methods in Engineering
Yes (verified by ORBilu)
[en] Collocation ; Interpolating moving least squares (IMLS) ; Meshfree ; Meshless ; Space-time ; Strong form ; Boundary conditions ; Initial value problems ; Ordinary differential equations ; Partial differential equations
[en] A novel space-time meshfree collocation method (STMCM) for solving systems of non-linear 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 that do not have any underlying mesh, but work on a set of nodes only without any a priori node-to-node connectivity. Instead, the neighbouring information is established on-the-fly. The STMCM is constructed using the Interpolating Moving Least-squares technique, which allows a simplified implementation of boundary conditions due to fulfillment of the Kronecker delta property by the kernel functions, which is not the case for the major part of other meshfree methods. The method is validated by several examples ranging from interpolation problems to the solution of PDEs, whereas the STMCM solutions are compared with either analytical or reference ones. © 2009 John Wiley & Sons, Ltd.

File(s) associated to this reference

Fulltext file(s):

Limited access
Netuzhylov_Zilian_2009_IJNME.pdfPublisher postprint1.11 MBRequest a copy

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.