Meshless methods: An overview and recent developments

Keywords

Discretization, Moving least squares, Quadrature (astronomy), Galerkin method, Collocation (remote sensing)

References

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• Continuous meshless approximations for nonconvex bodies by diffraction and transparencyD. Organ, Mark Fleming, Tara Terry — 1996
• Analysis of thin plates by the element-free Galerkin methodPetr Krysl, Ted Belytschko — 1995
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• A coupled finite element-element-free Galerkin methodTed Belytschko, D. Organ, Y. Krongauz — 1995
• Surfaces generated by moving least squares methodsPeter Lancaster, K. Šalkauskas — 1981
• Linking of Lagrangian particle methods to standard finite element methods for high velocity impact computationsGordon R. Johnson — 1994
• The Generalized Patch TestFriedrich Stummel — 1979
• Mixed‐Mode Fracture of Concrete Subjected to Impact LoadingReji John, Surendra P. Shah — 1990
• Reproducing kernel particle methods for structural dynamicsWing Kam Liu, Sukky Jun, Shaofan Li — 1995
• A stabilized finite point method for analysis of fluid mechanics problemsEugenio Oñate, Sergio R. Idelsohn, O.C. Zienkiewicz — 1996
• The finite difference method at arbitrary irregular grids and its application in applied mechanicsTadeusz Liszka, Janusz Orkisz — 1980
• Crack tip and associated domain integrals from momentum and energy balanceBrian J. Moran, C.F. Shih — 1987
• Computational crack path predictionYôichi Sumi — 1985
• Morphological aspects of fatigue crack propagation Part II—effects of stress biaxiality and welding residual stressYôichi Sumi, Yang Chen, Z. N. Wang — 1996

Cited by

• Computation of viscoelastic flow using neural networks and stochastic simulationD. Tran-Canh, T. Tran‐Cong — 2002
• A Pure Contour Formulation for the Meshless Local Boundary Integral Equation Method in ThermoelasticityJ. Sládek, V. Sládek, Satya N. Atluri — 2001
• Smoothed Particle Hydrodynamics Model for Diffusion through Porous MediaYi Zhu, Patrick J. Fox — 2001
• MLPG Analysis of Layered Composites with Piezoelectric and Piezomagnetic PhasesJ. Sládek, V. Sládek, S. Krahulec — 2012
• Four point explicit decoupled group iterative method applied to two-dimensional helmholtz equationMohd Kamalrulzaman Md Akhir, Mohamed Othman, Zanariah Abdul Majid — 2012
• Multifunctional Composite StructuresAshok V. Kumar — 2010
• OPTIMAL APPROXIMATION SPACES FOR SOLVING PROBLEMS WITH ROUGH COEFFICIENTSQiaoluan Helen Li — 2009
• A COUPLED MESHFREE/MESHBASED METHOD FOR COMPLEX FLUID-STRUCTURE INTERACTION PROBLEMSThomas‐Peter Fries, Hermann G. Matthies — 2005
• Simulation du soudage par friction et malaxage à l'aide de méthodes sans maillageAbdelaziz Timesli — 2013
• Modélisation numérique par la méthode SPH de la séparation eau-huile dans les séparateurs gravitairesNicolas Grenier — 2009
• Image-based physiological and statistical models of the heart: application to tetralogy of Fallot. (Modèles physiologiques et statistiques du cœur guidés par imagerie médicale : application à la tétralogie de Fallot)Tommaso Mansi — 2010
• Modeling of Intelligent Material Systems by the MLPGJ. Sládek, V. Sládek, P. Šolek — 2008
• Applications of the MLPG Method in Engineering &Sciences: A ReviewJ. Sládek, P. Staňák, Z-D. Han — 2013
• Meshless Local Petrov-Galerkin Method in Anisotropic ElasticityJ. Sládek, V. Sládek, Satya N. Atluri — 2004
• E(FG)2: a new fixed-grid shape optimization method based on the element-free galerkin mesh-free analysisFlorin Bobaru, Srinivas Rachakonda — 2006
• Meshless Local Petrov-Galerkin Micromechanical Analysis of Periodic Composites Including Shear LoadingsThi D. Dang, Bhavani V. Sankar — 2008
• Assessment of the applicability of XFEM in Abaqus for modeling crack growth in rubber.Luigi Gigliotti — 2012
• MLPG Method for Transient Heat Conduction Problem with MLS as Trial Approximation in Both Time and Space DomainsDavoud Mirzaei, Mehdi Dehghan — 2011
• Design of compliant mechanisms using meshless level set methodsZhen Luo, Nong Zhang, Tao Wu — 2012
• Micromechanical Study of Rock Fracture and Fragmentation under Dynamic Loads using Discrete Element MethodT. Kazerani — 2011

Related papers

• The New Collocation Meshless Method for Analyses of Forming ProblemsYong Ming Guo, Shunpei Kamitani — 2011
• The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticityV. Sládek, Tengteng Zhu, S. N. Atluri — 2000
• Numerical Implementation of Meshless Methods for Beam ProblemsVictoria Elena Roșca, Vitor M.A. Leitão — 2012
• Meshless Unsymmetric Collocation MethodLeevan Ling — 2008
• Direct meshless local Petrov-Galerkin method for elliptic interface problems with applications in electrostatic and elastostaticAmeneh Taleei, Mehdi Dehghan — 2014
• New concepts in meshless methodsSatya N. Atluri, Tulong Zhu — 2000
• The meshless regular hybrid boundary node method for 2D linear elasticityJianming Zhang, Zhenhan Yao, Masataka TANAKA — 2003
• New approximations and collocation schemes in the finite cloud methodXiaozhong Jin, Gang Li, N. R. Aluru — 2005
• A modified meshless local Petrov-Galerkin method to elasticity problems in computer modeling and simulationDie Hu, S.Y. Long, K.Y. Liu — 2006
• Meshless Galerkin least-squares methodXiaofei Pan, Xiong Zhang, Ming Lu — 2005