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Full Description
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.
Table of Contents
Meshless and Generalized Finite Element 1 (20)
Methods: A Survey of Some Major Results
I. Babuska
U. Banerjee
J. E. Osborn
Adaptive Meshfree Method of Backward 21 (16)
Characteristics for Nonlinear Transport
Equations
Jorn Behrens
Armin Iske
Martin Kaser
New Methods for Discontinuity and Crack 37 (14)
Modeling in EFG
Ted Belytschko
Giulio Ventura
Jingxiao Xu
SPH Simulations of MHD Shocks Using a 51 (12)
Piecewise Constant Smoothing Length Profile
Steinar Borve
Marianne Omang
Jan Trulsen
On the Numerical Solution of Linear 63 (12)
Advection-Diffusion Equation using Compactly
Supported Radial Basis Functions
Ismail Boztosun
Abdellatif Charafi
Dervis Boztosun
New RBF Collocation Methods and Kernel RBF 75 (12)
with Applications
Wen Chen
Tuned Local Regression Estimators for the 87 (18)
Numerical Solution of Differential Equations
Gary A. Dilts
Aamer Haque
John Wallin
Approximate Moving Least-Squares 105(12)
Approximation with Compactly Supported Radial
Weights
Gregory E. Fasshauer
Coupling Finite Elements and Particles for 117(14)
Adaptivity
Sonia Fernandez-Mendez
Antonio Huerta
A Hamiltonian Particle-Mesh Method for the 131(12)
Rotating Shallow-Water Equations
Jason Frank
Georg Gottwald
Sebastian Reich
Fast Multi-Level Meshless Methods Based on 143(18)
the Implicit Use of Radial Basis Functions
Csaba Gaspar
A Particle-Partition of Unity Method-Part IV: 161(32)
Parallelization
Michael Griebel
Marc Alexander Schweitzer
Some Studies of the Reproducing Kernel 193(18)
Particle Method
Weimin Han
Xueping Meng
Consistency by Correcting Coefficients in the 211(12)
Finite-Volume-Particle Method
Dietmar Hietel
Rainer Kech
Do Finite Volume Methods Need a Mesh? 223(16)
Michael Junk
An Upwind Finite Pointset Method (FPM) for 239(12)
Compressible Euler and Navier-Stokes Equations
Jorg Kuhnert
Adaptive Galerkin Particle Method 251(16)
Hongsheng Lu
Jiun-Shyan Chen
An Adaptivity Procedure Based on the Gradient 267(14)
of Strain Energy Density and its Application
in Meshless Methods
Yunhua Luo
Ulrich Haussler-Combe
New Developments in Smoothed Particle 281(10)
Hydrodynamics
Joseph J. Monaghan
The Distinct Element Method - Application to 291(16)
Structures in Jointed Rock
Joseph Morris
Lew Glenn
Stephen Blair
Advance Diffraction Method as a Tool for 307(12)
Solution of Complex Non-Convex Boundary
Problems
Boris Muravin
Eli Turkel
On the Stochastic Weighted Particle Method 319(8)
Endar H. Nugrahani
Sergej Rjasanow
The SPH/MLSPH Method for the Simulation of 327(12)
High Velocity Concrete Fragmentation
Timon Rabczuk
Josef Eibl
Lothar Stempniewski
Stability of DPD and SPH 339(20)
Philip W. Randles
Albert G. Petschek
Larry D. Libersky
Carl T. Dyka
A New Meshless Method - Finite-Cover Based 359(14)
Element Free Method
Rong Tian
Maotian Luan
Qing Yang
Finite Pointset Method Based on the 373(16)
Projection Method for Simulations of the
Incompressible Navier-Stokes Equations
Sudarshan Tiwari
Jorg Kuhnert
LPRH - Local Polynomial Regression 389(12)
Hydrodynamics
John F. Wallin
Aamer Haque
On Multigrid Methods for Generalized Finite 401(18)
Element Methods
Jinchao Xu
Ludmil T. Zikatanov
The Convergence of the Finite Mass Method for 419(22)
Flows in Given Force and Velocity Fields
Harry Yserentant
Survey of Multi-Scale Meshfree Particle 441(18)
Methods
Lucy T. Zhang
Wing K. Liu
Shao F. Li
Dong Qian
Su Hao
Appendix. Color Plates 459
