Progress on Meshless Methods PDF
Preview Progress on Meshless Methods
Progress 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:
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