Table Of ContentProgress on Meshless Methods
Computational Methods in Applied Sciences
Volume 11
Series Editor
E. Oñate
International Center for Numerical Methods in Engineering (CIMNE)
Technical University of Catalunya (UPC)
Edificio C-1, Campus Norte UPC
Gran Capitán, s/n
08034 Barcelona, Spain
A.J.M. Ferreira • E.J. Kansa
G.E. Fasshauer • V.M.A. Leitão
Editors
Progress on Meshless
Methods
Editors
A.J.M. Ferreira E.J. Kansa
Faculty of Engineering University of California
University of Porto Davis, California
Portugal USA
Preface
The term meshless (or meshfree) method refers to a broad class of effective numeri-
cal techniques for solving a growing number of science and engineering applications
without the dependence of an underlying computational mesh (as required by tra-
ditional methods such as finite elements or boundary elements). The variety of
problems analysed by these methods is very large, and ranges from fracture mechan-
ics, over fluid mechanics, multiscale problems, and laminated composites, all the
way to moving material interfaces, just to name a few.
In recent years, several international conferences have been held to foster the dis-
cussion of recent advances, share experiences with meshless methods and promote
new ideas in the field. The growing body of literature devoted to this area of research
provides clear evidence of the interest in meshless methods.
The objective of this book is to collect state-of-the-art papers contributing to the
development of this field of research. The book contains 17 invited papers written by
participants of the Second ECCOMAS Thematic Conference on Meshless Methods,
held in Porto, Portugal, from July 9th to 11th, 2007. The conference is one of a series
of Thematic Conferences sponsored by the European Community on Computational
Methods in Applied Sciences.
The list of contributors reveals a mix of highly distinguished authors as well as
young researchers who are very active working on promising results.
The editors hope that this book will constitute a valuable reference for researchers
in the field of mehless methods as applied to engineering and science problems.
The editors would like to thank all authors for their interesting contribution to
this book.
University of Porto, Portugal A.J.M. Ferreira
University of California-Davis, USA E.J. Kansa
Illinois Institute of Technology, USA G.E. Fasshauer
Instituto Superior Tecninco, Portugal V.M.A. Leitão
v
Contents
Particular Solution of Poisson Problems Using Cardinal Lagrangian
Polyharmonic Splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Barbara Bacchelli and Mira Bozzini
A Meshless Solution to the p-Laplace Equation . . . . . . . . . . . . . . . . . . . . . . 17
Francisco Manuel Bernal Martinez and Manuel Segura Kindelan
Localized Radial Basis Functions with Partition of Unity Properties . . . . . 37
Jiun-Shyan (JS) Chen, Wei Hu, and Hsin-Yun Hu
Preconditioning of Radial Basis Function Interpolation Systems
via Accelerated Iterated Approximate Moving Least Squares
Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Gregory E. Fasshauer and Jack G. Zhang
Arbitrary Precision Computations of Variations of Kansa’s Method . . . . . 77
Leevan Ling
A Meshless Approach for the Analysis of Orthotropic Shells
Using a Higher-Order Theory and an Optimization Technique . . . . . . . . . 85
Carla Maria da Cunha Roque, António Joaquim Mendes Ferreira,
and Renato Manuel Natal Jorge
An Order-N Complexity Meshless Algorithm Based on Local Hermitian
Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
David Stevens, Henry Power, and Herve Morvan
On the Determination of a Robin Boundary Coefficient in an Elastic
Cavity Using the MFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Carlos J.S. Alves and Nuno F.M. Martins
Several Meshless Solution Techniques for the Stokes Flow Equations . . . . 141
Csába Gáspár
vii
viii Contents
Orbital HP-Clouds for Quantum Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Jiun-Shyan Chen and Wei Hu
The Radial Natural Neighbours Interpolators Extended
to Elastoplasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Lúcia Maria de Jesus Dinis, Renato Manuel Natal Jorge, and Jorge Belinha
Static and Damage Analyses of Shear Deformable Laminated Composite
Plates Using the Radial Point Interpolation Method . . . . . . . . . . . . . . . . . . . 199
Armel Djeukou and Otto von Estorff
Analysis of Tensile Structures with the Element Free Galerkin Method . . 217
Bruno Figueiredo and Vitor M.A. Leitão
Towards an Isogeometric Meshless Natural Element Method . . . . . . . . . . . 237
David González, Elías Cueto, and Manuel Doblaré
A Partition of Unity-Based Multiscale Method . . . . . . . . . . . . . . . . . . . . . . . 259
Michael Macri and Suvranu De
Application of Smoothed Particle Hydrodynamics Method
in Engineering Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
Matej Vesenjak and Zoran Ren
Visualization of Meshless Simulations Using Fourier Volume
Rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
Andrew Corrigan, John Wallin, and Matej Vesenjak
Contributors
Carlos J.S. Alves
CEMAT-IST and Departamento de Matemática, Instituto Superior Técnico,
TULisbon, Avenida Rovisco Pais, 1096 Lisboa Codex, Portugal,
e-mail:
x Contributors
Suvranu De
Advanced Computational Research Laboratory, Department of Mechanical,
Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, 110,
8th Street, Troy, NY 12180, USA, e-mail:
Contributors xi
Manuel Segura Kindelan
G. Millán Institute for Modeling, Simulation and Industrial Mathematics,
Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain,
e-mail:
