A fast object-oriented Matlab implementation of the Reproducing Kernel Particle Method

Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems invo...

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Veröffentlicht in:Computational mechanics Jg. 49; H. 5; S. 581 - 602
Hauptverfasser: Barbieri, Ettore, Meo, Michele
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Berlin/Heidelberg Springer-Verlag 01.05.2012
Springer
Springer Nature B.V
Schlagworte:
Classical and Continuum Physics
Computation
Computational Science and Engineering
Cost analysis
Crack propagation
Deformation
Engineering
Finite element method
Kernels
Matrix algebra
Matrix methods
Meshless methods
Numerical methods
Original Paper
Shape functions
Stiffness matrix
Theoretical and Applied Mechanics
RKPM
Programming
Object-oriented
Meshless
ISSN:0178-7675, 1432-0924
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Zusammenfassung:Novel numerical methods, known as Meshless Methods or Meshfree Methods and, in a wider perspective, Partition of Unity Methods, promise to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes meshfree methods very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, meshfree methods still have significant limitations that prevent their acceptance among researchers and engineers, namely the computational costs. This paper presents an in-depth analysis of computational techniques to speed-up the computation of the shape functions in the Reproducing Kernel Particle Method and Moving Least Squares, with particular focus on their bottlenecks, like the neighbour search, the inversion of the moment matrix and the assembly of the stiffness matrix. The paper presents numerous computational solutions aimed at a considerable reduction of the computational times: the use of kd- trees for the neighbour search, sparse indexing of the nodes-points connectivity and, most importantly, the explicit and vectorized inversion of the moment matrix without using loops and numerical routines.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-011-0662-x