Progress on Meshless Methods

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A. J. M. Ferreira, E. J. Kansa, G. E. Fasshauer, V.M.A. Leitao
Springer Science & Business Media, Nov 23, 2008 - Technology & Engineering - 308 pages
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In recent years meshless/meshfree methods have gained considerable attention in engineering and applied mathematics. The variety of problems that are now being addressed by these techniques continues to expand and the quality of the results obtained demonstrates the effectiveness of many of the methods currently available. The book presents a significant sample of the state of the art in the field with methods that have reached a certain level of maturity while also addressing many open issues.

The book collects extended original contributions presented at the Second ECCOMAS Conference on Meshless Methods held in 2007 in Porto. The list of contributors reveals a fortunate mix of highly distinguished authors as well as quite young but very active and promising researchers, thus giving the reader an interesting and updated view of different meshless approximation methods and their range of applications. The material presented is appropriate for researchers, engineers, physicists, applied mathematicians and graduate students interested in this active research area.

 

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Contents

Particular Solution of Poisson Problems Using Cardinal Lagrangian Polyharmonic Splines
1
A Meshless Solution to the pLaplace Equation
17
Localized Radial Basis Functions with Partition of Unity Properties
36
Preconditioning of Radial Basis Function Interpolation Systems via Accelerated Iterated Approximate Moving Least Squares Approximation
57
Arbitrary Precision Computations of Variations of Kansas Method
77
A Meshless Approach for the Analysis of Orthotropic Shells Using a HigherOrder Theory and an Optimization Technique
84
An OrderN Complexity Meshless Algorithm Based on Local Hermitian Interpolation
99
On the Determination of a Robin Boundary Coefficient in an Elastic Cavity Using the MFS
125
Orbital HPClouds for Quantum Systems
159
The Radial Natural Neighbours Interpolators Extended to Elastoplasticity
174
Static and Damage Analyses of Shear Deformable Laminated Composite Plates Using the Radial Point Interpolation Method
199
Analysis of Tensile Structures with the Element Free Galerkin Method
217
Towards an Isogeometric Meshless Natural Element Method
237
A Partition of UnityBased Multiscale Method
259
Application of Smoothed Particle Hydrodynamics Method in Engineering Problems
273
Visualization of Meshless Simulations Using Fourier Volume Rendering
291

Several Meshless Solution Techniques for the Stokes Flow Equations
141

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