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Meshfree Methods for Partial Differential Equations

  • Conference proceedings
  • © 2003

Overview

Editors:
  1. Michael Griebel

    1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

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  2. Marc Alexander Schweitzer

    1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 26)

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Table of contents (30 papers)

  1. Front Matter

    Pages I-IX
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  2. Meshless and Generalized Finite Element Methods: A Survey of Some Major Results

    • I. Babuška, U. Banerjee, J. E. Osborn
    Pages 1-20

  3. Adaptive Meshfree Method of Backward Characteristics for Nonlinear Transport Equations

    • Jörn Behrens, Armin Iske, Martin Käser
    Pages 21-36

  4. New Methods for Discontinuity and Crack Modeling in EFG

    • Ted Belytschko, Giulio Ventura, Jingxiao Xu
    Pages 37-50

  5. SPH Simulations of MHD Shocks Using a Piecewise Constant Smoothing Length Profile

    • Steinar Børve, Marianne Omang, Jan Trulsen
    Pages 51-62

  6. On the Numerical Solution of Linear Advection-Diffusion Equation using Compactly Supported Radial Basis Functions

    • Ismail Boztosun, Abdellatif Charafi, Dervis Boztosun
    Pages 63-73

  7. New RBF Collocation Methods and Kernel RBF with Applications

    • Wen Chen
    Pages 75-86

  8. Tuned Local Regression Estimators for the Numerical Solution of Differential Equations

    • Gary A. Dilts, Aamer Haque, John Wallin
    Pages 87-104

  9. Approximate Moving Least-Squares Approximation with Compactly Supported Radial Weights

    • Gregory E. Fasshauer
    Pages 105-116

  10. Coupling Finite Elements and Particles for Adaptivity: An Application to Consistently Stabilized Convection-Diffusion

    • Sonia Fernández-Méndez, Antonio Huerta
    Pages 117-129

  11. A Hamiltonian Particle-Mesh Method for the Rotating Shallow-Water Equations

    • Jason Frank, Georg Gottwald, Sebastian Reich
    Pages 131-142

  12. Fast Multi-Level Meshless Methods Based on the Implicit Use of Radial Basis Functions

    • Csaba Gáspár
    Pages 143-160

  13. A Particle-Partition of Unity Method-Part IV: Parallelization

    • Michael Griebel, Marc Alexander Schweitzer
    Pages 161-192

  14. Some Studies of the Reproducing Kernel Particle Method

    • Weimin Han, Xueping Meng
    Pages 193-210

  15. Consistency by Coefficient-Correction in the Finite-Volume-Particle Method

    • Dietmar Hietel, Rainer Keck
    Pages 211-221

  16. Do Finite Volume Methods Need a Mesh?

    • Michael Junk
    Pages 223-238

  17. An Upwind Finite Pointset Method (FPM) for Compressible Euler and Navier-Stokes Equations

    • Jörg Kuhnert
    Pages 239-249

  18. Adaptive Galerkin Particle Method

    • Hongsheng Lu, Jiun-Shyan Chen
    Pages 251-265

  19. An Adaptivity Procedure Based on the Gradient of Strain Energy Density and its Application in Meshless Methods

    • Yunhua Luo, Ulrich Häussler-Combe
    Pages 267-279

  20. New Developments in Smoothed Particle Hydrodynamics

    • Joseph J. Monaghan
    Pages 281-290
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Keywords

About this book

Meshfree methods for the solution of partial differential equations gained much attention in recent years, not only in the engineering but also in the mathematics community. One of the reasons for this development is the fact that meshfree discretizations and particle models are often better suited to cope with geometric changes of the domain of interest, e.g. free surfaces and large deformations, than classical discretization techniques such as finite differences, finite elements or finite volumes. Another obvious advantage of meshfree discretizations is their independence of a mesh so that the costs of mesh generation are eliminated. Also, the treatment of time-dependent PDEs from a Lagrangian point of view and the coupling of particle models and continuous models gained enormous interest in recent years from a theoretical as well as from a practial point of view. This volume consists of articles which address the different meshfree methods (SPH, PUM, GFEM, EFGM, RKPM etc.) and their application in applied mathematics, physics and engineering.

Editors and Affiliations

  • Institut für Angewandte Mathematik, Universität Bonn, Bonn, Germany

    Michael Griebel, Marc Alexander Schweitzer

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